Question

A regular decagon has a radius of 8 cm.

What is the approximate area of the decagon? Recall that a decagon is a polygon with 10 sides.

188 cm2
198 cm2
304 cm2
375 cm2

Answer 1

Each of the 10 isosceles triangles with vertex at the center has area (1/2)R^2 sin(central angle). The central angle = 360°/10 = 36°, so

Area = 10 * (1/2) * 8^2 * sin36° = 5 * 64 * sin36° = 320 * sin36° ≈ 320 * 0.587785 = 188.1 cm^2.

So the closest choice is 188 cm^2.