Question

The height of an equilateral triangle is 6 cm . Find its area

Answer 1

Side×side = Formula of area of equilateral triangle
6×6=36

Answer 2

$\huge\underline{\pink{A}\blue{N}\red{S}\purple{W}\orange{E}\green{R}}$

Given

The height of an equilateral triangle is 6 cm.

Find

The area of equilateral triangle.

SOLUTION

As, given triangle is equilateral

$AB=BC=AC=a$

$Also, BD=\frac{1}{2}BC=\frac{a}{2}$

In a right angled triangle ADB

$AD^2+BD^2=AB^2$

$6^2+(\frac{a}{2})$

$⇒ 36=\frac{3a^2}{4}$

on simplifying we get

$a^2=36\times \frac{4}{3}$

$=48$

∴ Area of equilateral triangle is

$=\frac{\sqrt3}{4}\times a^2=\frac{\sqrt3}{4}\times</p><p> 48$

$=12\sqrt3cm^2$

HOPE IT HELPS!!