Question

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 below). If the sides of the wall are 15 m, 11 m and 6 m, find the area painted in colour.

Answer 1

We are given a triangle with the following sides:

• Side 1 = 15 m
• Side 2 = 11 m
• Side 3 = 6 m

We need to find the area of the painted wall.

Step-by-Step Solution:

1. Calculate the Semi-perimeter (s):

The semi-perimeter \( s \) of the triangle is given by the formula: \[ s = \frac{a + b + c}{2} \] where: - \( a = 15 \, \text{m} \), - \( b = 11 \, \text{m} \), - \( c = 6 \, \text{m} \). Substituting the values: \[ s = \frac{15 + 11 + 6}{2} = \frac{32}{2} = 16 \, \text{m} \]

2. Apply Heron's Formula to Find the Area:

Heron's formula for the area \( A \) of a triangle is: \[ A = \sqrt{s(s - a)(s - b)(s - c)} \] Substituting the values of \( s \), \( a \), \( b \), and \( c \): \[ A = \sqrt{16(16 - 15)(16 - 11)(16 - 6)} \] Simplifying: \[ A = \sqrt{16 \times 1 \times 5 \times 10} \] \[ A = \sqrt{16 \times 50} = \sqrt{800} \] \[ A = 28.28 \, \text{m}^2 \]

Final Answer:

The area of the painted region is \( \boxed{28.28 \, \text{m}^2} \).