# 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.

**Solution:**

Given: Dimensions of the triangular wall.

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

The sides of the triangular walls are a = 11 m, b = 6 m and c = 15 m.

Semi Perimeter:

s = (a + b + c)/2

= (11 + 6 + 15)/2

= 32/2

= 16 m

By using Heron’s formula,

Area of triangular wall = √s(s - a)(s - b)(s - c)

Substituting the given values in formula,

= √16(16 -11)(16 - 6)(16 -15)

= √16 × 5 × 10 × 1

= √800 m²

= 20√2 m²

Area of the wall of the park to be painted in colour = 20√2 m^{2}.

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

**Video Solution:**

## 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.

Class 9 Maths NCERT Solutions Chapter 12 Exercise 12.1 Question 3

**Summary:**

It is given that 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”. The sides of the wall are 15 m, 11 m and 6 m and we have found that the area painted in colour 20√2 sq. m.

**☛ 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?
- Find the area of a triangle two sides of which are 18cm and 10cm and the perimeter is 42cm.
- Sides of a triangle are in the ratio of 12:17:25 and its perimeter is 540cm. Find its area.

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