Question

if the area of an equilateral triangle is 81√3cmsq, find it's height

Answer 1

Given that area of an equilateral triangle is 81√3cmsq.

To find the height we need to use area of equilateral triangle formula which is

$Area = \frac{\sqrt{3}}{4}a^2$ where "a" is the side of triangle.

plug the given area

$81 \sqrt{3} = \frac{\sqrt{3}}{4}a^2$

$81 \sqrt{3} = \frac{\sqrt{3}}{4}a^2$

$81 \sqrt{3}*\frac{4}{\sqrt{3}} = a^2$

$81 *4= a^2$

$324= a^2$

$\sqrt{324}= a$

18=a

We also know that area of triangle is given by formula

$Area = \frac{1}{2}bh$

where b=base=a=18

h=height

so plug those values

$81 \sqrt{3} = \frac{1}{2}*18h$

$81 \sqrt{3} = 9h$

$9 \sqrt{3} = h$

Hence final height is $9 \sqrt{3}$ cm.

Answer 2

Area of equilateral =√3/4x^2
81√3*4/√3=x^2
x^2=a*2=18cm

=area of =1/2*AD*BC
81√3=1/2*h*18
9√3*1/9=h
h=9√3cm.