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

Given:

Perimeter = 60 cm

Let a be the sides of equilateral triangle.

Perimeter = Sum of all sides

⇒ 60 = a + a + a

⇒ 60 = 3a

⇒ a = $\dfrac{60}{3}$

⇒ a = 20 cm

Area of equilateral triangle = $\dfrac{\sqrt{3}}{4} \times side^2$

$= \dfrac{\sqrt{3}}{4} \times 20^2\\[1em] = \dfrac{\sqrt{3}}{4} \times 400\\[1em] = 100 \sqrt{3} \\[1em] = 173.2 cm^2$

Height of equilateral triangle = $\dfrac{\sqrt{3}}{2} \times side$

$= \dfrac{\sqrt{3}}{2} \times 20\\[1em] = 10 \sqrt{3}\\[1em] = 17.32 cm$

Hence, the area is 173.2 cm² and the perimeter is 17.32 cm.