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

**Solution:**

Given: Equal sides of the triangle and its perimeter.

Heron's formula for the area of a triangle is: Area = √s(s - a)(s - b)(s - c)

Where a, b, and c are the sides of the triangle, and s = Semi-perimeter = Half the perimeter of the triangle

Equal sides: a = b = 12 cm (given)

The formula for the perimeter of a triangle: Perimeter(P) = a + b + c

30 = 12 + 12 + c (Given, perimeter = 30 cm)

c = 30 - 24

c = 6 cm

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

s = 30/2

s = 15 cm

By using Heron’s formula,

Area of a triangle = √s(s - a)(s - b)(s - c)

= √15(15 - 12)(15 -12)(15 - 6)

= √15 × 3 × 3 × 9

= √1215

= 9√15 cm^{2}

Area of the triangle = 9√15 cm^{2}

**Video Solution:**

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

### Class 9 Maths NCERT Solutions - Chapter 12 Exercise 12.1 Question 6:

**Summary:**

It is given that there is an isosceles triangle that has a perimeter of 30 cm and each of the equal sides is 12 cm. We have found that its area is 9√15 cm^{2}.