Question

By Herons formula Find the area of an equilateral triangle whose perimeter is 60cm

Answer 1

Perimeter = 3a
60 = 3a
a = 20cm.

s = (a+b+c)÷2
s = 30

Area= √s(s-a)(s-b)(s-c)
= √30 × 10 ×10×10 =√ 3 × 10 ×10×10×10 = 100√3 cm²

Answer 2

find the side of the equilateral triangle =60/3=20cm
according to herons formula
area=root of (s*(s-a) *(s-b) *(s-c))
Here s is half the perimeter =60/2=30
now as it is equilateral all sides a b and c are each 20cm
put the values
a=root of (30*10*10*10)
a=root of 3*root of 10000
a=root 3*100
a=1.732*100=173.2cm2