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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: Q8. (page 431)

Find the area of each figure:

Short Answer

Expert verified

The area of given figure is24 square units.

Step by step solution

01

Step 1. Given information.

Given figure is a rhombus.

The side of rhombus is 5 and one of its diagonal is 8.

02

Step 2. Concept used.

Area of rhombus can be found using the diagonals

$A = \frac{1}{2} d_{1} d_{2}$

Where $d_{1} d_{2}$ , are the two diagonals of rhombus.

03

Step 3. Find the diagonal of rhombus.

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 $△ A O B$

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

$5^{2} = 4^{2} + O B^{2}$

$25 = 16 + O B^{2}$

$O B^{2} = 9$

$O B = 3$

Thus, the another diagonal is $B D = O B + O D = 3 + 3 = 6$

04

Step 4. Find the area of given figure.

Area of the rhombus

$A = \frac{1}{2} d_{1} d_{2}$

$= \frac{1}{2} \times 6 \times 8$

$= 24$ Square units.

Therefore, the area of given figure is 24square units.

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Most popular questions from this chapter

Use a calculator or the trigonometry table on page 311to find the area of each figure to the nearest tenth.

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

Find the area of given figure?

$\bar{F G}$ is the altitude to the hypotenuse of $△ D E F$ . Name three similar triangles and find their areas. (Hint: See Theorem $8 - 1$ and Corollary 1on pages). $285 - 286$

The base of a rectangle is 16cmand perimeter is42cm. What is the area and height of the rectangle?

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