Show that among regular polygons having the same perimeter, the area increases with the number of sides

Q: find the perimeter (to the nearest centimeter) of a rrgular 7-sided polygon inscribed in a circle…

A: According to the given problem the represented diagram is shown below. Let each side of the polygon…

Q: Find the area of the regular polygon.

A: given  apothem = 15 side of pentagon = 18   Perimeter = 5 * 18 = 90

Q: Show that of all the rectangles with a given perimeter,the one with greatest area is a square.

A: Let the perimeter P is given.  Let, length = x and width= y So, 2(x+y)=P Or, x+y=P/2 Or, y= (P/2) -…

Q: 4. Find the area of the largest isosceles trapezoid inscribed in a semicircle of radius 4 inches if…

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Q: Prove that the area of a circle circumscribed about a square is twice the area of the circle…

A: Prove that the area of a circle circumscribed about a square is twice the area of the circle…

Q: Find the dimensions of the rectangle of largest area that can be inscribed in a circle of radius r.

A: Consider a rectangle, inscribed in a circle of radius r.Then,

Q: Find the area of the largest isosceles trapezoid inscribed in a semicircle of radius 4 inches if its…

A: Area of trapezoid

Q: What is the largest area of a rectangle inscribed in a circle of radius a?

A: To find the largest area of a rectangle inscribed in a circle of radius a.

Q: if a triangle is inscribed in a circle so that one of the triangle side is a diameter of a circle,…

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Q: Show that all the rectangles with a given perimeter , the square has the largest area

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Q: Find the area of an octagon if the distance from center to vertex is 25 in.

A: The area of regular octagon with circumradius r(distance from center to vertex ): A = 22r2

Q: Find the area of the largest rectangle that fits inside a circle of radius 3

A: Given: Radius of a circle r=3

Q: Find the area of the regular pentagon.

A: The question is taken from the areas of the different shapes in which we have to find the area of…

Q: In a certain isosceles right triangle, the altitude to the hypotenuse has length 4sqrt2. What is the…

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Q: find the area of the largest square that can be cut from a circle of radius of 4 in

A: To Determine: find the area of the largest square that can be cut from a circle of radius of 4…

Q: (a) Find the smallest perimeter possible for a rectangle whose area is 25in? and what are its…

A: Due to q & a guidelines I will answer for only 1st question

Q: How many diagonals are there in a polygon of 10 sides?

A:

Q: If an open box is made from a square tin sheet 12×12 in. by cutting an identical squares from each…

A: in this question, there is an open box made by 12*12in  tin sheet For the box to be of the largest…

Q: Generalize Exercise 42 to the case of an n-sided polygon inscribed in a circle of radius r. Express…

A: An n-sided polygon inscribed in a circle of radius r.

Q: Calculate the area of the regular polygon if s is 10 metres and a is 8.0 metres.

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Q: 13 Find the area of the rectangle of largest area that can be inscribed in a semicircle of radius 6.

A: We first consider a semicircle with center at (0,0) and radius = 6  It will have equation:

Q: Find the area of the largest circle which can be cut from a square of edge 5 in. What is the area of…

A: square edge(L) = 5 in.Area of square = L^2= 5*5= 25 sq.inthe center of the square will be the center…

Q: What is the area of the largest rectangle that can fit inside of a circle of radius R?

A: Let x and y be the length of ABCD that can be fit inside a circle of radius R  Then AB=x and BC=y…

Q: Find the area of the largest rectangle that can be inscribed in a circle of radius 20 cm.

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Q: Find the area of the largest rectangle that fits inside a semicircle with a radius of 4.

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Q: Find the perimeter of a regular octagon inscribed in a circle of radius 150 cm.

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Q: What is the area of a hexagon that is inscribed in a circle if the area of the circle is 170 m2 ?

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Q: Find the area of the largest rectangle that can be inscribed in asemicircle of radius r

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Q: What is the total area of the original unfolded rectangle as shown if the total area of the figure…

A: To find the total area of the original unfolded rectangle as shown if the total area of the figure…

Q: Show how the formula for the area of a parallelogram can be obtained from the formula for the area…

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Q: Find the point that partitions segment AB in a 2 : 1 ratio.

A: Given that partition of segment AB in a  2:1 ratio . Where coordinates of point A  and B are 1,3 and…

Q: Find the area of inscribed circle of a regular hexagon whose side has length 8.

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Q: Find the dimensions of the isosceles triangle of largest areathat can be inscribed in a circle of…

A: here first we make a circle of radius r and inside this make an isosceles triangle. This is shown in…

Q: Determine the dimensions of the rectangle of largest area that can be inscribed in the right…

A: Given the figure:

Q: Find the area of the largest rectangle that can be inscribed in a semicircle of radius 10cm.

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Q: What is the largest absolute difference between the areas of two of the right triangles that can be…

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Q: Find the area of the regular polygon

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Q: Show that of all n-gons having the same perimeter, the regular n-gon has the greatest area. Show…

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Q: he corners of a 2-meter square are cut off to form a regular octagon. What is the length of the…

A: Given : The corners of a 2-meter square are cut off to form a regular octagon.   To find the…

Q: If the perimeter of a semi circular protractor is 108 cm , FInd the diamteer of the protracator

A: Perimeter of Semicircular Protractor = 108 cm

Q: Find the dimensions of the rectangle of largest area that can be inscribed in a circle of radius r .

A:

Q: What is the smallest perimeter possible for a rectangle whose area is 16 in2, and what are its…

A: Let l be the length and b be the breadth of the rectangle.

Q: 2. Find the area of the largest square that can be cut from a circle of radius of 4 in.

A: given,

Q: Find the exact area of the regular hexagon whose sides have length 18m.

A: We are given the sides of a regular hexagon is 18 m. Now, we need to find the area of the given…

Q: rectangle

A: The diameter of circular sheet will be equal to the diagonal of of rectangle.

Q: Find the area (in squared units) of the largest trapezoid that can be inscribed in a circle of…

A: Given: The radius of circle is 3 units. The base is the diameter of the circle.

Q: Determine the dimensions of the largest rectangle that could be inscribed in a semi-circle of radius…

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Q: What is the height of the isosceles triangle with the greatest area that can be inscribed in a…

A: In order to solve the given question first we need to find a function in terms of a variable and…

Q: Assuming that the (square) base of this building has a side length of 646 feet and that the pyramid…

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…