Question

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

Answer 1

in a right angled triangle ABD:
AD²+BD²=AB² = (6)²+(a/2)²=a²
on simplifying we get
a²=36x4/3=48
therefore area of equilateral triangle
=√3/4x48cm²=12√3

Answer 2

Answer:

$\text{Area of equilateral triangle is }\frac{12\sqrt3cm^2}$

Step-by-step explanation:

Given the height of an equilateral triangle is 6 cm.

we have to find the area of equilateral triangle.

As, given triangle is equilateral

AB=BC=AC=a

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

In a right angled triangle ADB

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

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

⇒ $36=\frac{3a^2}{4}$

on simplifying we get

$a^2=36\times \frac{4}{3}=48$

∴ Area of equilateral triangle is  

$=\frac{\sqrt3}{4}\times a^2=\frac{\sqrt3}{4}\times 48=12\sqrt3cm^2$