Question

Find the area of equilateral triangle whose perimeter is 30 cm

Answer 1

Perimeter of an equilateral triangle = 30 cm

Side of an equilateral triangle = 30/3 = 10cm

Area of equilateral triangle = √3 / 4 x (side)^2

                                           = √3 / 4 x 10 x 10

                                           = 25√3

                                           = 25x 1.732cm square

                                           

Answer 2

Given: Perimeter is 30 cm.

To find: The area of equilateral triangle whose perimeter is 30 cm.

Solution:

The perimeter given is of an equilateral triangle which means that all the sides are equal in length. Let the length of one side be equal to x. Hence, x can be calculated using the formula of perimeter given below.

$perimeter = x+x+x$

$30 = 3x$

$x= 10 cm$

So, the length of the side of the triangle is 10 cm. Now, the height of the triangle must be calculated using the following formula.

$height = \frac{\sqrt{3} }{2} a$

Here, a is the length of the side of the triangle.

$height = \frac{\sqrt{3} }{2} (10)$

          $= 8.66 cm$

Now, the area is calculated as follows.

$Area = \frac{1}{2} *b*h$

        $= \frac{1}{2} * 10 *8.66$

        $=43.3 cm^{2}$

Therefore, the area of equilateral triangle whose perimeter is 30 cm is 43.3 cm².