Question

Each side of an equilateral triangle is 10 cm. Find (i) the area of the triangle and (ii) the height of the triangle.

Answer 1

(1)The area of the equilateral triangle=`sqrt3/4xx"side"^2` 

=`sqrt3/4xx10^2` 

=`sqrt3/4xx100` 

=`25sqrt3 cm^2` 

or `25xx1.732=43.3cm^2` 

So, the area of the triangle is  `25sqrt3 cm^2  or  433cm^2` 

(2) As, area of the equilateral triangle =`25sqrt3 cm^2` 

⇒`1/2xx "Base" xx "Height"=25sqrt3` 

⇒` 1/2xx10xx"Height"=25sqrt3`  

⇒ `5xx"Height"=25sqrt3` 

⇒`"Height" =(25sqrt3)/5=5sqrt3` 

Or `"Height" = 5xx1.732=8.66m` 

∴ The height of the triangle  is `5sqrt3 cm or 8.66 cm`