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Geometry

Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

$Math Studyset Vaia Explanations$ Math

Student Edition · 227 pages

ISBN: 9780395977279

Chapter 11: Q18. (page 431)

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

Short Answer

Expert verified

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

Step by step solution

01

Step 1. Given information.

Perimeter of regular hexagon is60 .

02

Step 2. Analyze the given information.

Regular Hexagon has six equal sides.

Let the side of hexagon be

So, we can conclude

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

$\Rightarrow 6 a = 60$

$\Rightarrow a = 10$

03

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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Most popular questions from this chapter

The base of a rectangle is $5 \sqrt{3}$ and height $2 \sqrt{3}$ .What is the area?

The base of a rectangle is 8cmand height 3cm.What is the area?

Find the area of each figure:

An isosceles triangle with sides $10, 10, 16$

The perimeter of a square is $28 c m$ .What is the area?

a. Use the diagram at the right. Find the area of $▱ P Q R S$ .

b. Use the diagram at the right. Find the area of $△ P S R$ .

c. Use the diagram at the right. Find the area of $△ O S R$ . (Hint: Refer to $△ P S R$ and use Exercise28).

d. Use the diagram at the right. What is the area of $△ P S O$ ?

e. Use the diagram at the right. What must the area of $△ P O Q$ be? Why? What must the area of $△ O Q R$ be?

f. Use the diagram at the right. State what you have shown in parts (a)-(e) about how the diagonals of a parallelogram divide the parallelogram.

See all solutions

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