can you please help me find the answer

Question

Find the area of the figure.  Round to the nearest hundreth.

A=  mm²

Answer 1

Using SOH-CAH-TOA, we have 5 triangles, each with a hypotenuse of 20, which split the pentagon using lines connecting the center to the pentagon's sides.

If we split each of these triangles in half with a perpendicular from the center to each side, we have 10 right triangles. The area of each is (1/2)*20*sin(36 degrees)*20*cos(36 degrees) = 951.06 square mm, rounded to 2 decimal places of accuracy.

Answer 2

There are 5 isosceles triangles in the area.

The central angle is 72 degrees. (360/5)

The area of one of the triangles is (1/2)*20*20*sin 72.