# Find the area of a triangle two sides of which are 18cm and 10cm and the perimeter is 42cm.

**Solution:**

Given: Two sides of the triangle and its perimeter.

By using Heron’s formula, we can calculate the area of triangle.

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

The sides of triangle given: a =18 cm, b = 10 cm

Perimeter of the triangle = (a + b + c)

42 = 18 + 10 + c

42 = 28 + c

c = 42 - 28

c = 14 cm

Semi Perimeter

s = (a + b + c) = 42/2 = 21 cm

By using Heron’s formula,

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

= √21(21 - 18)(21 - 10)(21 - 14)

= √21 × 3 × 11 × 7

= 21√11 cm^{2}

Area of the triangle = 21√11 cm^{2}.

**Video Solution:**

## Find the area of a triangle two sides of which are 18cm and 10cm and the perimeter is 42cm.

### Class 9 Maths NCERT Solutions - Chapter 12 Exercise 12.1 Question 4:

**Summary:**

It is given that in a given triangle two sides are 18cm and 10cm and the perimeter is 42cm. We have found its area equal to 21√11 cm^{2}.