Question

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

Answer 1

Let ABC be the given equilateral triangle and AD is perpendicular to base BC ; then clearly AD= √6cm
If each side of the given triangle be a cm then AB= a cm
and BD= 1/2 of BC
BD=1/2a cm
In right angle triangle ABD :
AD^2+BD^2=AB^2
(√6)^2+(a/2)^2=a^2


On simplifying,we get : a^2 = 6/3= 2

Area of the triangle = √3/4 a^2
=√3/4 × 2 cm square
= √3/2 cm square.