Question

A regular pentagon has an apothem measuring 3 cm and a perimeter of 21.8 cm. What is the area of the pentagon, rounded to the nearest tenth? 13.8 cm2 17.3 cm2 32.7 cm2 69.0 cm2

Answer 1

Option C) 32.7 cm square

Explanation:

We are given the following information in the question:

Apothegm of regular pentagon = 3 cm

Perimeter of regular pentagon = 21.7 cm

Area of regular pentagon =

`\displaystyle(1)/(2)* \text{Perimeter} * \text{Apothegm}\\\\(1)/(2)* 21.7 * 3 = 32.7~cm^2`

Hence, the area of regular pentagon is 32.7 cm square.

Answer 2

The area of a regular polygon is given by
A = (1/2)Pa
where P is the perimeter, and "a" is the apothem.

For your numbers, the area is
A = (1/2)(21.8 cm)(3 cm) = 32.7 cm²