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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: Q. 9 (page 431)

Find the area of each figure:

Short Answer

Expert verified

The area of given figure is 84 square unit.

Step by step solution

01

Step 1. Given information.

02

Step 2. Use Phythagoras theorem.

Using Pythagoras theorem finding the missing leg of the triangles first and second.

In first triangle:

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

$13^{2} = 5^{2} + B^{2}$

$B^{2} = 169 - 25$

$B^{2} = 144$

$B = 12$

In the second triangle

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

$15^{2} = P^{2} + 12^{2}$

$P^{2} = 225 - 144$

$P^{2} = 81$

$P = 9$

03

Step 3. Concept used.

Area of triangle can be found using the formula

$A = \frac{1}{2} b h$

Where,

b= Base of a triangle and h= Height of a triangle

04

Step 4. Find the area of first triangle.

$A_{1} = \frac{1}{2} b h$

$= \frac{1}{2} \times 12 \times 5$

$= 6 \times 5$

=30 Square unit

05

Step 5. Find the area of second triangle.

$A_{2} = \frac{1}{2} b h$

$= \frac{1}{2} \times 9 \times 12$

$= 9 \times 6$

=54 Square unit

06

Step 6. Find the total area.

Total area of given figure

$A = A_{1} + A_{2}$

$= 30 + 54$

=84 Square unit

Therefore, the area of given figure is84 Square unit.

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Most popular questions from this chapter

a. An equilateral triangle has sides of length s. Show that its area is $\frac{s^{2}}{4} \sqrt{3}$

b. Find the area of an equilateral triangle with side 7

The base of a rectangle is 16cmand area is $80 c m^{2}$ .What is the height?

If the area of $▱ P Q R S$ is 36and Tis a point on $\bar{P Q}$ . Find the area of $△ R S T$ (Hint: Draw a diagram.)

Find the area of each figure:

Consecutive sides of the figures are perpendicular. Find the area of each figure.

See all solutions

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