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Q18.

Expert-verified

Geometry

Found in: Page 431

Book edition Student Edition

Author(s) Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

Pages 227 pages

ISBN 9780395977279

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Short Answer

Find the area of each figure:
A regular hexagon with perimeter 60 .

The area of given figure is $150 \sqrt{3}$ square units.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information.

Perimeter of regular hexagon is60 .

Step 2. Analyze the given information.

Regular Hexagon has six equal sides.

Let the side of hexagon be

So, we can conclude

$a + a + a + a + a + a = 60$

$\Rightarrow 6 a = 60$

$\Rightarrow a = 10$

Step 3. Find the area of given figure.

Area of regular hexagon can be found using the formula

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

$= \frac{3 \sqrt{3}}{2} {(10)}^{2}$

$= \frac{3 \sqrt{3}}{2} \times 100$

$= 150 \sqrt{3}$ Square units.

Therefore, the area of given figure is $150 \sqrt{3}$ square units.

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Find the area of each figure:

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