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All Textbook Solutions for Elementary Geometry for College Students

Find the measure of a central angle of a regular polygon of a 8 sides. c 9 sides. b 10 sides. d 12 sides.Find the number of sides of a regular polygon that has a central angle measuring a 90. c 60. b 45. d 24.Find the number of sides of a regular polygon that has a central angle measuring a 30. c 36. b 72. d 20.Find the measure of each interior angle of a regular polygon whose central angle measures a 40. c 45.Find the measure of each interior angle of a regular polygon whose central angle measures a 60. c 90.23E Find the measure of each exterior angle of a regular polygon whose central angle measures a 45. c 120.Find the number of sides for a regular polygon in which the measure of each interior angle is 60 greater than the measure of each central angle.Find the number of sides for a regular polygon in which the measure of each interior angle is 90 greater than the measure of each central angle.Is there a regular polygon for which each central angle measures a 40? c 60? b 50? d 70?Given regular hexagon ABCDEF with each side of length 6, find the length of diagonal AC. Hint: With G on AC , draw BGAC.Given regular octagon RSTUVWXY with each side of length 4, find the length of diagonal RU. HINT: Extended sides, as shown, form a square.Given that RSTVQ is a regular pentagon and PQR is equilateral in the figure shown, determine a the type of triangle represented by VPQ. b the type of quadrilateral represented by TVPS.Given: Regular pentagon RSTVQ with equilateral PQR Find: mVPS Given: Regular pentagon JKLMN not shown with diagonals LNandKN. Find: mLNK Is there a regular polygon with 8 diagonals? If so, how many sides does it have?34E 35E Find the measure of a central angle of a regular polygon that has 35 diagonals.In Review Exercises 1 to 6, use the figure shown. Construct a right triangle so that one leg has length AB and the other leg has length twice AB.2CR In Review Exercises 1 to 6, use the figure shown. Construct an isosceles triangle with vertex angle B and legs the length of AB from the line segment shown.4CR 5CR 6CR 7CR 8CR 9CR 10CR 11CR 12CR 13CR 14CR 15CR 16CR 17CR 18CR 19CR 20CR 21CR 22CR 23CR 24CR 25CR 26CR 27CR In a regular polygon, each central angle measures 45. a How many sides does the regular polygon have? b How many diagonals does this regular polygon have? c If each side measures 5 cm and each apothem is approximately 6 cm in length, what is the perimeter of the polygon?29CR 30CR Can a circle be inscribed in each of the following figures? a Parallelogram c Rectangle b Rhombus d Square The length of the radius of a circle inscribed in an equilateral triangle is 7 in. Find the length of the radius of the triangle.33CR 34CR Draw and describe the locus of points in the plane that are equidistant from parallel lines l and m. _________________________________________ ________________________________________2CT 3CT 4CT Describe the locus of points in space that are at a distance of 3 cm from point P. ________________________________________ ___________________________________________6CT For a given triangle such as ABC, what word describes the point of concurrency for athe three perpendicular bisectors of sides? _____________ bthe three altitudes? ____________________8CT Which of the following must be concurrent at an interior point of any triangle? angle bisectors perpendicular bisectors of sides altitudes medians ___________________________________Classify as true/false: aA circle can be inscribed in any regular polygon.________________ bA regular polygon can be circumscribed about any circle. _______________ cA circle can be inscribed in any rectangle. ____________ dA circle can be circumscribed about any rhombus. __________________11CT 12CT 13CT For a regular octagon, the length of the apothem is approximately 12 cm and the length of the radius is approximately 13 cm. To the nearest centimeter, find the perimeter of the regular octagon. ________________________For a regular hexagon ABCDEF, the length of side AB is 4 in. Find the exact length of adiagonal AC. _________________ bdiagonal AD. ______________For rectangle MNPQ, points A, B, C and D are the midpoints of the sides. aWhat type of quadrilateral not shown is ABCD? _____________________ bAre the inscribed circle for ABCD and the circumscribed circle for MNPQ concentric circles? _____________________17CT Suppose that two triangles have equal areas. Are the triangles congruent? Why or why not? Are two squares with equal areas necessarily congruent? Why or why not?The area of the square is 12, and the area of the circle is 30. Does the area of the entire shaded region equal 42? Why or why not?Consider the information in Exercise 2, but suppose you know that the area of the region defined by the intersection of the square and the circle measures 5. What is the area of the entire colored region? 2. The area of the square is 12, and the area of the circle is 30. Does the area of the entire shaded region equal 42? Why or why not?If MNPQ is a rhombus, which formula from this section should be used to calculate its area? Exercise 46 In rhombus MNPQ, how does the length of the altitude from Q to PN compare to the length of the altitude from Q to MN? Explain. Exercises 46 When the diagonals of rhombus MNPQ are drawn, how do the areas of the four resulting smaller triangles compare to each other and to the area of the given rhombus? Exercise 46 7E Are ABC and DEF congruent? Exercises 7, 8 9E In Exercises 9 to 18, find the areas of the figures shown or described. A right triangle has one leg measuring 20 in. and a hypotenuse measuring 29 in.In Exercises 9 to 18, find the areas of the figures shown or described. A 454590 triangle has a leg measuring 6 m.12E In Exercises 9 to 18, find the areas of the figures shown or described. ABCD In Exercises 9 to 18, find the areas of the figures shown or described. EFGH In Exercises 9 to 18, find the areas of the figures shown or described.In Exercises 9 to 18, find the areas of the figures shown or described.In Exercises 9 to 18, find the areas of the figures shown or described.18E In Exercises 19 to 22, find the area of the shaded region.20E In Exercises 19 to 22, find the area of the shaded region. PQST In Exercises 19 to 22, find the area of the shaded region. A and B are midpoints.A triangular corner of a store has been roped off to be used as an area for displaying Christmas ornaments. Find the area of the display section.Carpeting is to be purchased for the family room and hallway shown. What is the area to be covered?The exterior wall the gabled end of the house shown remains to be painted. a What is the area of the outside wall? b If each gallon of paint covers approximately 105ft2, how many gallons of paint must be purchased? c If each gallon of paint is on sale for 22.50, what is the total cost of the paint?The roof of the house shown needs to be reshingled. a Considering that the front and back sections of the roof have equal areas, find the total area to be reshingled. b If roofing is sold in squares each covering 100ft2, how many squares are needed to complete the work? c To remove old shingles and replace with new shingles costs 97.50 per square. What is the cost of reroofing?A beach tent is designed so that one side is open. Find the number of square feet of canvas needed to make the tent.Gary and Carolyn plan to build the deck shown. a Find the total floor space area of the deck. b Find the approximate cost of building the deck if the estimated cost is 6.40 per ft2.A square yard is a square with sides 1 yard in length. a How many square feet are in 1 square yard? b How many square inches are in 1 square yard?The following problem is based on this theorem: A median of a triangle separates it into two triangles of equal area. In the figure, RST has median RV. a Explain why ARSV=ARVT. b If ARST=40.8cm2, find ARSV.31E 32E 33E In Exercises 34 to 36, provide paragraph proofs. Given: Right ABC Prove: h=abc In Exercises 34 to 36, provide paragraph proofs. Given: Square HJKL with LJ=d Prove: AHJKL=d22 In Exercises 34 to 36, provide paragraph proofs. Given: RSTV with VWVT Prove: ARSTV=(RS)2 Given: The area of right ABC not shown is 40in2. mC=90 AC=x BC=x+2 Find: x The lengths of the legs of a right triangle are consecutive even integers. The numerical value of the area is three times that of the longer leg. Find the lengths of the legs of the triangle.Given: ABC, whose sides are 13 in., 14 in., and 15 in. Find: a BD, the length of the altitude to the 14-in. side HINT: USE the Pythagorean Theorem twice. b The area of ABC, using the result from part a Exercises 39, 40 40E If the length of the base of a rectangle is increased by 20 percent and the length of the altitude is increased by 30 percent, by what percentage is the area increased?If the length of the base of a rectangle is increased by 20 percent but the length of the altitude is decreased by 30 percent, by what percentage is the area changed? Is this an increase or a decrease in area?43E 44E The algebra method of FOIL multiplication is illustrated geometrically in the drawing. Use the drawing with rectangular regions to complete the following rule: (a+b)(c+d)=Use the square configuration to complete the following algebra rule: (a+b)2= NOTE: Simplify where possible.In Exercises 47 to 50, use the fact that the area of the polygon is unique. In the right triangle, find the length of the altitude drawn to the hypotenuse.48E 49E In Exercises 47 to 50, use the fact that the area of the polygon is unique. In ABCD,AB=7 and BC=12. The length of altitude AF to side BC is 5. Find the length of altitude AE from A to DC.The area of a rectangle is 48in2. Where x is the width and y is the length, express the perimeter P of the rectangle in terms only of x.The perimeter of the rectangle is 32 cm. Where x is the width and y is the length, express the area A of the rectangle in terms only of x.Square DEFG is inscribed in right ABC, as shown. If AD=6 and EB=8, find the area of square DEFG.TV bisects STR of STR. ST=6 and TR=9. If the area of STR is 25m2, find the area of SVT.55E 56E In Exercises 1 to 8, find the perimeter of each polygon.In Exercises 1 to 8, find the perimeter of each polygon.In Exercises 1 to 8, find the perimeter of each polygon. ABCD with ABBC d1=4md2=10m In Exercises 1 to 8, find the perimeter of each polygon In Exercises 1 to 8, find the perimeter of each polygon.In Exercises 1 to 8, find the perimeter of each polygon.In Exercises 1 to 8, find the perimeter of each polygon.In Exercises 1 to 8, find the perimeter of each polygon.In Exercises 9 and 10, use Herons Formula. Find the area of a triangle whose sides measure 13 in., 14 in., and 15 in.10E For Exercises 11 and 12, use Brahmaguptas Formula. For cyclic quadrilateral ABCD, find the area if AB=39 mm, BC=52 mm, CD=25 mm, and DA=60 mm.For Exercises 11 and 12, use Brahmaguptas Formula. For cyclic quadrilateral ABCD, find the area if AB=6 cm, BC=7 cm, CD=2 cm, and DA=9 cm.13E In Exercises 13 to 18, find the area of the given polygon.15E 16E In Exercises 13 to 18, find the area of the given polygon. kite ABCD with BD=12 mBAC=45,mBCA=30 18E In a triangle of perimeter 76 in., the length of the first side is twice the length of the second side, and the length of the third side is 12 in. more than the length of the second side. Find the lengths of the three sides.In a triangle whose area is 72 in2, the base has a length of 8 in. Find the length of the corresponding altitude.A trapezoid has an area of 96 cm2. If the altitude has a length of 8 cm and one base has a length of 9 cm, find the length of the other base.The numerical difference between the area of a square and the perimeter of that square is 32. Find the length of a side of the square.23E Find the ratio A1A2 of the areas of two similar rectangles if a the ratio of the lengths of the corresponding sides is S1S2=25. b the length of the first rectangle is 6 m, and the length of the second rectangle is 4 m.In Exercises 25 and 26, give a paragraph form of proof. Provide drawings as needed. Given: Equilateral ABC with each side of length s Prove: AABC=S243 HINT: Use Herons Formula.In Exercises 25 and 26, give a paragraph form of proof. Provide drawings as needed. Given: Isosceles MNQ with QM=QN=s and MN=2a Prove: AMNQ=as2-a2 NOTE: sa.In Exercises 27 to 30, find the area of the figure shown. Given: In O, OA=5, BC=6, and CD=4 Find: AABCD In Exercises 27 to 30, find the area of the figure shown. Given: Hexagon RSTVWX with WV-XT-RS- RS=10 ST=8 TV=5 WV=16 WX-VT- Find: ARSTVWX In Exercises 27 to 30, find the area of the figure shown. Given: Pentagon ABCDE with DC-DE- AE=AB=5 BC=12 Find: AABCDE In Exercises 27 to 30, find the area of the figure shown. Given: Pentagon RSTVW with mVRS=mVSR=60,RS=82, and RW-WV-VT-TS- Find: ARSTVW Mary Frances has a rectangular garden plot that encloses an area of 48 yd2. If 28 yd of fencing are purchased to enclose the garden, what are the dimensions of the rectangular plot?32E Farmer Watson wishes to fence a rectangular plot of ground measuring 245 ft by 140 ft. aWhat amount of fencing is needed? bWhat is the total cost of the fencing if it costs 1.59 per foot?The farmer in Exercise 33 has decided to take the fencing purchased and use it to enclose the subdivided plots shown. aWhat are the overall dimensions of the rectangular enclosure shown? bWhat is the total area of the enclosure shown?35E Find the perimeter of the room in Exercise 35.Examine several rectangles, each with a perimeter of 40 in., and find the dimensions of the rectangle that has the largest area. What type of figure has the largest area?Examine several rectangles, each with an area of 36 in2, and find the dimensions of the rectangle that has the smallest perimeter. What type of figure has the smallest perimeter?Square RSTV is inscribed in square WXYZ, as shown. If ZT=5 and TY=12, find athe perimeter of RSTV bthe area of RSTV Exercises 39, 40 Square RSTV is inscribed in square WXYZ, as shown. If ZT=8 and TY=15, Find athe perimeter of RSTV bthe area of RSTV For Exercises 41 and 42, the sides of square ABCD are trisected at the indicated points. Find the ratio: a PEGIKPABCD b AEGIKAABCD Exercises 41 and 42 For Exercises 41 and 42, the sides of square ABCD are trisected at the indicated points. Find the ratio: a PEHILPABCD b AEHILAABCD Exercises 41 and 42 43E 44E For Exercises 45 and 46, use this information: Let a, b, and c be the integer lengths of the sides of a triangle. If the area of the triangle is also an integer, then a, b, c is known as a Heron triple. Which of these are Heron triples? a 5, 6, 7 b 13, 14, 15 46E 47E 48E For Exercises 48 and 49, use the formula found in Exercise 47. Find the area of a trapezoid with an altitude of length 513ft and a median of length 214ft.Prove that the area of a square whose diagonal has length d is A=12d2.51E 52E The shaded region is that of a trapezoid. Determine the height of the trapezoid.4 Trapezoid ABCD not shown is inscribed in O so that side DC- is a diameter of O. If DC=10 and AB=6, find the exact area of trapezoid ABCD.Each side of square RSTV has length 8. Point W lies on VR- and point Y lies on TS- in such a way to form parallelogram VWSY, which has an area of 16units2. Find the length of VW-.For the cyclic quadrilateral MNPQ, the sides have lengths a, b, c, and d. If a2+b2=c2+d2, explain why the area of the quadrilateral is A=ab+cd2.Find the area of a square with a sides of length 3.5 cm each. b apothem of length 4.7 in.Find the area of a square with a a perimeter of 14.8 cm. b radius of length 42 in.Find the area of an equilateral triangle with a sides of length 2.5 m each. b apothem of length 3 in.Find the area of an equiangular triangle with a a perimeter of 24.6 cm. b radius of length 4 in.In a regular polygon, each central angle measures 30. If each side of the regular polygon measures 5.7 in., find the perimeter of the polygon.In a regular polygon, each interior angle measures 135. If each side of the regular polygon measures 4.2 cm, find the perimeter of the polygon.For a regular hexagon, the length of the apothem is 10 cm. Find the length of the radius for the circumscribed circle for this hexagon.For a regular hexagon, the length of the radius is 12 in. Find the length of the radius for the inscribed circle for this hexagon.In a particular type of regular polygon, the length of the radius is exactly the same as the length of a side of the polygon. What type of regular polygon is it?In a particular type of regular polygon, the length of the apothem is exactly one-half the length of a side. What type of regular polygon is it?11E If the area (A=12aP) and the perimeter of a regular polygon are numerically equal, find the length of the apothem of the regular polygon.Find the area of a square with apothem a = 3.2 cm and perimeter P = 25.6 cm.Find the area of an equilateral triangle with apothem a = 3.2 cm and perimeter P=19.23 cm.Find the area of an equilateral triangle with apothem a = 4.6 in. and perimeter P=27.63 in.Find the area of a square with apothem a = 8.2 ft and perimeter P = 65.6 ft.In Exercises 17 to 30, use the formula A=12aP to find the area of the regular polygon described. Find the area of a regular pentagon with an apothem of length a = 5.2 cm and each side of length s = 7.5 cm.In Exercises 17 to 30, use the formula A=12aP to find the area of the regular polygon described. Find the area of a regular pentagon with an apothem of length a = 6.5 in. and each side of length s = 9.4 in.In Exercises 17 to 30, use the formula A=12aP to find the area of the regular polygon described. Find the area of a regular octagon with an apothem of length a = 9.8 in. and each side of length s = 8.1 in.In Exercises 17 to 30, use the formula A=12aP to find the area of the regular polygon described. Find the area of a regular octagon with an apothem of length a = 7.9 ft and each side of length s = 6.5 ft.21E In Exercises 17 to 30, use the formula A=12aP to find the area of the regular polygon described. Find the area of a square whose apothem measures 5 cm.In Exercises 17 to 30, use the formula A=12aP to find the area of the regular polygon described. Find the area of an equilateral triangle whose radius measures 10 in.In Exercises 17 to 30, use the formula A=12aP to find the area of the regular polygon described. Find the approximate area of a regular pentagon whose apothem measures 6 in. and each of whose sides measures approximately 8.9 in.In Exercises 17 to 30, use the formula A=12aP to find the area of the regular polygon described. In a regular octagon, the approximate ratio of the length of an apothem to the length of a side is 6:5. For a regular octagon with an apothem of length 15 cm, find the approximate area.In Exercises 17 to 30, use the formula A=12aP to find the area of the regular polygon described. In a regular dodecagon 12 sides, the approximate ratio of the length of an apothem to the length of a side is 15:8. For a regular dodecagon with a side of length 12 ft, find the approximate area.In Exercises 17 to 30, use the formula A=12aP to find the area of the regular polygon described. In a regular dodecagon 12 sides, the approximate ratio of the length of an apothem to the length of a side is 15:8. For a regular dodecagon with an apothem of length 12 ft, find the approximate area.In Exercises 17 to 30, use the formula A=12aP to find the area of the regular polygon described. In a regular octagon, the approximate ratio of the length of an apothem to the length of a side is 6:5. For a regular octagon with a side of length 15 ft, find the approximate area.In Exercises 17 to 30, use the formula A=12aP to find the area of the regular polygon described. In a regular polygon of 12 sides, the measure of each side is 2 in., and the measure of an apothem is exactly (2+3)in. Find the exact area of this regular polygon.In Exercises 17 to 30, use the formula A=12aP to find the area of the regular polygon described. In a regular octagon, the measure of each apothem is 4 cm, and each side measures exactly 8(21) cm. Find the exact area of this regular polygon.Find the ratio of the area of a square circumscribed about a circle to the area of a square inscribed in the circle.Given regular hexagon ABCDEF with each side of the length 6 and the diagonal AC, find the area of pentagon ACDEF.Given a regular octagon RSTUVWXY with each side of length 4 and diagonal RU, find the area of hexagon RYXWVU.Regular octagon ABCDEFGH is inscribed in a circle whose radius is 722 cm. Considering that the area of the octagon is less than the area of the circle and greater than the area of the square ACEG, find the two integers between which the area of the octagon must lie. Note: For the circle, use A=r2 with227.Given regular pentagon RSTVQ and equilateral triangle PQR, and the length of an apothem not shown of RSTVQ is 12, while the length of each side of the equilateral triangle is 10, find the approximate area of the kite VPST.Consider regular pentagon RSTVQ not shown. Given that diagonals QT and VR intersect at point F, show that VFFR=TFFQ.37E The length of each side of a regular hexagon measures 6in. Find the area of the inscribed regular hexagram shaded in the figure.Find the exact circumference and area of a circle whose radius has length 8 cm.Find the exact circumference and area of a circle whose diameter has length 10 in.3E Find the approximate circumference and area of a circle whose diameter has length 20 cm. Use =3.14.Find the exact lengths of the radius and the diameter of a circle whose circumference is: a 44 in b 60 ft Find the approximate lengths of the radius and the diameter of a circle whose circumference is: a88 in. Use =227. b 157 m Use =3.14.Find the exact lengths of the radius and the diameter of a circle whose area is: a 25 in2 b 2.25 cm2 Find the exact length of the radius and the exact circumference of a circle whose area is: a 36 m2 b 6.25 ft2 Find exactly lAB, where AB refers to the minor arc of the circle.10E 11E Use your calculator value of to find the approximate area of a circle with radius length 12.38 in.13E 14E 15E 16E 17E A rectangle has an area of 36 in2. What is the limit smallest possible value of the perimeter of the rectangle?The legs of an isosceles triangle each measure 10 cm. What are the limit of the length of the base.Two sides of a triangle measure 5 in and 7 in. What are the limits of the length of the third side.Let N be any point on side BC of the right triangle ABC. Find the upper and lower limits for the length of AN.What is the limit of mRTS if T lies in the interior of the shaded region?In exercises 23-26, find the exact areas of shaded region. Square inscribed in a circle In exercises 23-26, find the exact areas of shaded region.In exercises 23-26, find the exact areas of shaded region. d1=30 ft d2=40 ft Rhombus In exercises 23-26, find the exact areas of the shaded regions. Regular hexagon inscribed in a circle In Exercises 27 and 28, use your calculator value of to solve each problem. Round answers to the nearest integer. Find the length of the radius of the circle whose area is 154 cm2.28E 29E The ratio of the circumferences of two circles is 2:1. What is ratio of their areas?Given concentric circles with radii of lengths R and r, where Rr, explain why Aring=(r+r)(Rr).32E The radii of two concentric circles differ in length by exactly 1 in. If their areas differ by exactly 7 in2, find the lengths of the radii of the two circles.34E 35E In Exercises 34-44, use your calculator value of unless otherwise stated. Round answers to two decimal places. A track is to be constructed around the football field at a high school. If the straightaways are 100 yd in length, what length of radius is needed for each of the semicircle shown if the total length around the track is to be 440 yd.37E 38E 39E In Exercises 34-44, use your calculator value of unless otherwise stated. Round answers to two decimal places. In a two pulley system, the center of the pulleys is 20 in apart. If the radius of the each pulley measures 6 in., how long is the belt used in the pulley system.41E 42E In Exercises 34-44, use your calculator value of unless otherwise stated. Round answers to two decimal places. A communications satellite forms a circular orbit 375 mi above the earth. If the earths radius is approximately 4000 mi. What distance is travelled by the satellite in one complete orbit.44E The diameter of a carousel merry-go-round is 30ft. At full speed, it makes a complete revolution in 6 s. At what rate, in feet per second, is a horse on the outer edge moving?A tabletop is semicircular when its three congruent drop-leaves are used. By how much has the tables area increased when the drop leaves increased. Give the answer to the nearest whole percent.Given that the length of each side of a rhombus is 8 cm and that an interior angle measures 60. Find the area of the inscribed circle.Given O with radii OA- and OB- and chord AB-. aWhat type of figure sector or segment is bounded by OA-, OB- and AB? bIf OA=7 cm and lAB=11 cm, find the perimeter of the figure in a.2E In the semicircular region shaded DQ=6". a Find the exact perimeter of the region. b Find the exact area of the region.For the semicircular region of Exercise 3, the length of the radius is r. a Find an expression for the perimeter of the region. b Find an expression for the area of the region.In the circle, the radius length is 10 in. and the length of AB is 14 in. What is the perimeter of the shaded sector?If the area of the circle is 360 in2, what is the area of the sector if its central angle measures 900?If the area of 1200 sector is 50 cm2, what is the area of the entire circle?If the area of the 1200 sector is 40 cm2 and the area of MON is 16 cm2, what is the area of the segment bounded by MN- and MN?9E Suppose a circle of radius r is inscribed in a rhombus, each of whose sides has length s. Find an expression for the area of the rhombus in terms of r and s.Find the perimeter of a segment of a circle whose boundaries are a chord measuring 24 mm millimetres and an arc of length 30 mm.12E A circle is inscribed in a triangle having sides of lengths 6 in., 8 in., 10 in. If the length of the radius of the inscribed circle is 2 in., find the area of the triangle.A circle is inscribed in a triangle having sides of lengths 5 in., 12 in., and 13 in. If the length of the radius of inscribed circle is 2 in., find the area of the triangle.A triangle with sides of lengths 3 in., 4 in., and 5 in., has an area of 6 in2. What is the length of the radius of the inscribed circle?The approximate area of a triangle with sides of lengths 3 in., 5 in., and 6 in. is 7.48 in2. What is the approximate length of the radius of the inscribed circle?Find the exact perimeter and area of the sector shown.Find the exact perimeter and area of the sector shown.19E Find the approximate area of the sector shown. Answer to the nearest hundredth of a square inch.Find the exact perimeter and area of the segment shown, given that mO=600 and OA=12 in.22E In Exercises 23 and 24, find the exact areas of the shaded regions.In Exercises 23 and 24, find the exact areas of the shaded regions.Assuming that the exact area of a sector determined by a 400 arc is 94 cm2, find the length of the radius of the circle.26E A circle can be inscribed in the trapezoid shown. Find the area of that circle.28E In a circle whose radius has length 12 m, the length of an arc is 6 m. What is the degree measure of that arc?At the Pizza Dude restaurant, a 12-in. pizza costs 5.40 to make, and the manager wants to make at least 4.80 from the sale of each pizza. If the pizza will be sold by the slice and each pizza is cut into 6 pieces, what is the minimum charge per slice?31E Determine a formula for the area of the shaded region determined by the square and its inscribed circle.Determine a formula for the area of the shaded region determined by the circle and its inscribed square.

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