Calculate the area and the height of an equilateral triangle whose perimeter is 60 cm.

Given:

Perimeter = 60 cm

Let the length of each side of an equilateral triangle be 'a' cm.

Perimeter = Sum of all sides

⇒ 60 = a + a + a

⇒ 60 = 3a

⇒ a = $\dfrac{60}{3}$ = 20 cm.

$\Rightarrow \text{Area of equilateral triangle} = \dfrac{\sqrt{3}}{4} \times \text{ side}^2 \\[1em] = \dfrac{\sqrt{3}}{4} \times 20^2 \\[1em] = \dfrac{\sqrt{3}}{4} \times 400 \\[1em] = 100 \sqrt{3} \\[1em] = 173.2 \text{ cm}^2.$

By formula,

$\text{Height of an equilateral triangle} = \dfrac{\sqrt{3}}{2} \times \text{ side} \\[1em] = \dfrac{\sqrt{3}}{2} \times 20 \\[1em] = 10 \sqrt{3} \\[1em] = 17.32 \text{ cm}.$

Hence, the area of triangle = 173.2 cm² and the height = 17.32 cm.