Q12. - Geometry

Question

Find the area of each figure:

An equilateral triangle with perimeter.18

Step-by-Step Solution

Answer

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

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.

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

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

       $=\sqrt{3}\times 3\times 3$ 

    $=9\sqrt{3}$  Square units.

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