# An isosceles triangle has perimeter 30 cm and each of the equal sides is 12 cm. Find the area of the triangle.

Given

The length of two equal sides of an isosceles triangle is 12 cm.

Perimeter = 30 cm.

Find out

We have to determine the area of a triangle

Formula

By using Heron’s formula, area of triangle= $$\sqrt{s(s-a)(s-b)(s-c)}$$

Solution

The length of third side = (Perimeter)-(length of two side)

= 30-(12+12)

= 6 cm

a = 12 cm

b = 12 cm

c = 6 cm

Semi Perimeter (s) = (a+b+c)/2

s = (12+12+6)/2

s = 15 cm

ar(△ABC) = √s(s-a)(s-b)(s-c)

= √15(15-12)(15-12)(15-6)

= √15×(3)×(3)×(9)

= 9√15 cm2

Hence, the area of triangle is 9√15 cm2