*trigonometry and area*
find the area of a regular pentagon with a side length of 8cm. round to the nearest tenth

110.1 cm^2 to nearest tenth.

Explanation:

The area  consists of 5 isosceles triangles with base angles 1/2 * 108 = 54 degrees.

Using trigonometry to find the height of these triangles:

tan 54 = h / (1/2 * 8)

tan 54 = h / 4

h = 4 tan 54

h = 5.506 cm.

The area of a triangle = 4 * 5.506 = 22.024 cm^2

So the area of the pentagon 5 * 22.024

= 110.12 cm^2.