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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: Q16. (page 431)

Find the area of each figure:
An equilateral triangle with height9

Short Answer

Expert verified

The area of given figure is $27 \sqrt{3}$ square units.

Step by step solution

01

Step 1. Given information.

An equilateral triangle with height 9

Here, $h = 9$

02

Step 2. Find the side of triangle.

We can use Pythagorean Theorem.

Pythagorean Theorem define that in a right angle triangle, the square of the hypotenuse is equal to the sum of squares of other sides.

$H^{2} = P^{2} + B^{2}$

$a^{2} = h^{2} + {(\frac{a}{2})}^{2}$

$a^{2} - \frac{a^{2}}{4} = h^{2}$

$\frac{3 a^{2}}{4} = h^{2}$

$\frac{3 a^{2}}{4} = h^{2} 3 a^{2} = 4 h^{2}$

$a = \frac{2}{\sqrt{3}} h$

$a = \frac{2}{\sqrt{3}} \times 9$

$a = 6 \sqrt{3}$

03

Step 3. Find the area of given figure.

$A = \frac{\sqrt{3}}{4} a^{2}$

$= \frac{\sqrt{3}}{4} {(6 \sqrt{3})}^{2}$

$= \frac{108 \sqrt{3}}{4}$

$= 27 \sqrt{3}$ Square units.

Therefore, the area of given figure is $27 \sqrt{3}$ square units.

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Most popular questions from this chapter

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.

Find the area of each figure:

A rectangle with length $16$ inscribed in a circle with radius $10$ .

The base of a rectangle is $3 \sqrt{2}$ and height $4 \sqrt{2}$ .What is the area?

The base of a rectangle is $x + 3$ and height X.What is the area?

Find the area of each figure:

An isosceles right triangle with hypotenuse 8

See all solutions

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