Question

A regular pentagon has an apothem measuring 20 cm and a perimeter of 145. 3 cm. A rectangular pentagon has an apothem measuring 20 centimeters and a perimeter of 145. 3 centimeters. What is the area of the pentagon? square centimeters.

Answer 1

The area of the pentagon is 1,453 squared centimeters.

Given information-

The length of the apothem of a regular pentagon is 20 cm.

The measure of the perimeter of a regular pentagon is 145.3 cm.

The length of the apothem of a rectangular pentagon is 20 cm.

The measure of the perimeter of a rectangular pentagon is 145.3 cm.

Pentagon-

Pentagon is the closed shaped polygon which has 5 sides. When these 5 sides are equal in length then the pentagon is called teh regular pentagon. When four of the sides of pentagon make a rectangle then the pentagon is called the rectangular pentagon.

Area of regular pentagon-

Area of regular pentagon is half of the product of its apothem and perimeter. It can be given as,

$A=\dfrac{1}{2} \times 20\times 145.3\\A=1453$

Thus the area of the pentagon is 1,453 squared centimeters.

Learn more about the regular pentagon here;

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