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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: Q6. (page 431)

Find the area of each figure:

Short Answer

Expert verified

The area of given figure is12 square units.

Step by step solution

01

Step 1. Given information.

The sides of triangle are given $5, 5$ and6 .

02

Step 2. 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

03

Step 3. Find the Height of a 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.

Using Pythagorean Theorem in $△ A B D$

$A B^{2} = B D^{2} + A D^{2}$

$5^{2} = 3^{2} + A D^{2}$

$25 = 9 + A D^{2}$

$A D^{2} = 16$

$A D = 4$

04

Step 4. Find the area of given figure.

Area of the triangle

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

$= \frac{1}{2} \times 6 \times 4$

$= 12$ Square units.

Therefore, the area of given figure is 12square units.

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