from a handpicked tutor in LIVE 1-to-1 classes

# 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}.

**☛ Check: **Class 9 Maths NCERT Solutions Chapter 12

**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}.

**☛ Related Questions:**

- A traffic signal board, indicating ‘SCHOOL AHEAD’, is an equilateral triangle with side ‘a’. Find the area of the signal board, using Heron’s formula. If its perimeter is 180 cm, what will be the area of the signal board?
- The triangular side walls of a flyover have been used for advertisements. The sides of the walls are 122 m, 22 m, and 120 m (see Fig. 12.9). The advertisements yield an earning of ₹ 5000 per m2 per year. A company hired one of its walls for 3 months. How much rent did it pay?
- There is a slide in a park. One of its side walls has been painted in some colour with a message “KEEP THE PARK GREEN AND CLEAN” (see Fig. 12.10). If the sides of the wall are 15 m, 11 m and 6 m, find the area painted in colour.
- An isosceles triangle has perimeter 30 cm and each of the equal sides is 12 cm. Find the area of the triangle.

visual curriculum