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Q12.

Expert-verified
Found in: Page 431

### Geometry

Book edition Student Edition
Author(s) Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen
Pages 227 pages
ISBN 9780395977279

# Find the area of each figure:An equilateral triangle with perimeter.18

The area of given figure is$9\sqrt{3}$ square units.

See the step by step solution

## Step 1. Analyze the given information.

Let the common sides be x

We know that in equilateral triangle all three sides are equal in length.

The perimeter of equilateral triangle18, which means the sum of all three sides will be equal to 18

$x+x+x=18$

$3x=18$

$x=6$

Thus, the sides of triangle are

$6,6,6$

## Step 2. Concept used.

Area of an equilateral triangle can be found using the formula

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

Where,

a=The sides of triangle.

## Step 3. Find the area of given figure.

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

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

$=\sqrt{3}×3×3$

$=9\sqrt{3}$ Square units.

Therefore, the area of given figure is$9\sqrt{3}$ square units.