Question

Find the area of the regular pentagon with radius 19 mm.

Answer 1

Answer: 8.58 cm²

Explanation:

The area of the central triangle bounded by each of the sides can be computed as ...

A = (1/2)r²sin(α) . . . . where α is the central angle, 360°/5 = 72°

There are 5 such triangles, so the area of the pentagon is

A = (5/2)(1.9 cm)²sin(72°) ≈ 8.58 cm²

Answer 2

621.09 mm²

Explanation:

Area of pentagon =
`((perimeter) (apothem))/(2)`

Let's solve

`((5 times 19) times 13.08)/(2)` = 621.09 mm²

So, the answer is 621.09 mm²