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.

Answer 2

The area of a regular decagon with side length of 8 centimetre to the nearest whole number is about 492 cm².

What is a regular decagon?

A regular decagon is a polygon that has 10 sides and the angles are congruent.

Therefore,

area of regular decagon = 1 / 2 pa

where

• a = apothem
• p = perimeter

Therefore,

a = s / 2 tan (180 / n)

where

• s = side length
• n = number of sides

Therefore,

a = 8 / 2 tan (180 / 10)

a = 8 / 0.64983939246

a = 12.3114804555

a = 12.311 cm

perimeter = 8 × 10 = 80cm

area of the regular decagon = 1 /  2 × 12.311 × 80

area of the regular decagon = 984.918436442 / 2

area of the regular decagon = 492.459218221

area of the regular decagon ≈ 492 cm²

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