Question

What is the area of the regular 15-gon with radius 12mm?

Answer 1

The regular pentagon can divide into 5 congruent isosceles triangles

The equal sides of each triangle have length r and vertex angle of measure 72 degrees

Then we will use the sine rule of the area to find the area of each triangle, then multiply it by 5 to get the area of the pentagon

Since the radius is 7mm, then

r = 7

`A=5*(1)/(2)* r* r* sin72`

Substitute r by 7

`\begin{gathered} A=5*(1)/(2)*7*7* sin72 \\ \\ A=116.5044232\text{ mm}^2 \end{gathered}`

Round it to the nearest whole number

A = 117 mm^2

The area of the pentagon is 117 mm^2