Question

A regular decagon has sides that are 8 cm long. What is the area of the figure? Round to the nearest whole number.

Answer 1

Given:

Given that the regular decagon has sides that are 8 cm long.

We need to determine the area of the regular decagon.

Area of the regular decagon:

The area of the regular decagon can be determined using the formula,

$A=\frac{s^{2} n}{4 \tan \left(\frac{180}{n}\right)}$

where s is the length of the side and n is the number of sides.

Substituting s = 8 and n = 10, we get;

$A=\frac{8^{2} \times 10}{4 \tan \left(\frac{180}{10}\right)}$

Simplifying, we get;

$A=\frac{64 \times 10}{4 (\tan \ 18)}$

$A=\frac{640}{4 (0.325)}$

$A=\frac{640}{1.3}$

$A=642.3$

Rounding off to the nearest whole number, we get;

$A=642 \ cm^2$

Thus, the area of the regular decagon is 642 cm²

Hence, Option B is the correct answer.