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 m2.
☛ 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:
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- 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.