Question

The altitude of an equilateral triangle is 4 cm, then
the area of triangle is:​

Answer 1

Step-by-step explanation:

Let ABC be a right angled triangle,

and AD be the altitude.

we know that altitude of equilateral triangle is bisector.

so, BD= CD

AND, AB= 1/2 BD

by pythagoras theorm,

AD^2= AB^2 + BD^2

4^2 = AB^2 + ( 1/2AB)^2

16 = AB^2 +1/4AB^2

16= 5/4AB^2

AB^2 = (16×4)/5

AB^2 = 64/5

AB= 8/√5 cm

AREA = 1/2×BASE×HEIGHT

area = 1/2× 8/√5× 4

area= 16/√5 cm^2