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Area and Perimeter Practice Test 3

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Question : 3 of 40

Marks: +1, -0

f the area of a regular hexagon is

96 \sqrt{3} m^{2}

, find its side.

2 m
4 m
6 m
8 m

Solution:

Concept:

The area of a regular hexagon is related to its side

a

by

A = \frac{3\sqrt{3}}{2}a^2

.

Explanation:

Given area

A = 96\sqrt{3}\ \mathrm{m}^2

.

Use the formula:

\frac{3\sqrt{3}}{2}a^2 = 96\sqrt{3}

.

Cancel

\sqrt{3}

from both sides:

\frac{3}{2}a^2 = 96

.

Multiply both sides by

2

:

3a^2 = 192

.

Divide both sides by

3

:

a^2 = 64

.

Take the positive square root:

a = 8\ \mathrm{m}

.

Answer:

The side of the regular hexagon is

8\ \mathrm{m}

(Option D).

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