Question

The perimeter and area of a regular pentagon with side lengths of 6 and an apothem of 7

Answer 1

Answer:

The formula for the perimeter of a regular polygon:

P = sn

Where P is perimeter, s is side length, and n is number of sides.

Since this is a pentagon, n is 5. The side length is given: 6.

So, P = 6 x 5.

Multiply.

This means the perimeter is 30.

The formula for the area of a regular polygon:

A = 1/2Pa

Where P is perimeter and a is apothem.

We already found perimeter, which is 30, and the apothem is given, 7.

So, A = 1/2 x 30 x 7

Multiply.

The area of the pentagon is 105.