Exercises deal with a regular
a.Show that the perimeter P of a regular n-gon inscribed in a circle of radius r is
b.What is the circumference (perimeter) of a circle of radius
c.Calculate P in part (a) with
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College Algebra and Trigonometry (4th Edition)
- 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?arrow_forwardIn 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.arrow_forwarda Given that the polygon shown has six congruent angles, this polygon is known as an __________ _________ b What is the measure of each of the congruent interior angles?arrow_forward
- 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.arrow_forwardIn terms of the apothem a and length of side s of the smaller regular pentagon, find an expression for the shaded area.arrow_forwarda Are any two regular pentagons similar? b Are any two equiangular pentagons similar?arrow_forward
- Use Exercise 33 and the following drawing to complete the proof of this theorem: The length of the median of a trapezoid is one-half the sum of the lengths of the two bases. Given: Trapezoid ABCD with median MN Prove: MN=12(AB+CD) 33. Use Theorem 5.6.1 and the drawing to complete the proof of this theorem: If a line is parallel to one side of a triangle and passes through the midpoint of a second side, then it will pass through the midpoint of the third side. Given: RST with M the midpoint of RS;MNST Prove: N is the midpoint of RTarrow_forwardIf 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?arrow_forwardIf AC is a diameter of O, find the area of the shaded triangle. Exercise 17arrow_forward
- Complete the following table for regular polygons. Number of sides 8 12 20 Measure of each exterior 24 36 Measure of each interior 157.5 178 Number of diagonalsarrow_forwardIn 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.arrow_forwardIn 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.arrow_forward
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