Question

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

Answer 1

Let the side of the equilateral triangle be x cm. 

As, the area of an equilateral triangle = `sqrt3/4 "(side)"^2=(x^2sqrt3)/4` 

Also, the area of the triangle =`1/2xxBasexxHeight=1/2xx x xx6=3x` 

So, `(x^2sqrt3)/4=3x` 

⇒` (xsqrt3)/4=3` 

⇒`x=12/sqrt3` 

⇒`x=12/sqrt3xxsqrt3/sqrt3` 

⇒`x=(12sqrt3)/3` 

⇒` x=4sqrt3 cm` 

Now, area of the equilateral triangle =3x 

=`3xx4sqrt3` 

=`12sqrt3` 

=`12xx1.73` 

=`20.76 cm^2`