Question

There is a slide in a park. One of its side walls has been painted in some color with a message “KEEP THE PARK GREEN AND CLEAN” (see figure). If the sides of the wall are 15m, 11m, and 6m. Find the area painted in green color.

Answer 1

Hint: In this particular question use the concept that if all the sides of the triangle are given then the area (A) of the triangle is given as, $A = \sqrt {s\left( {s - a} \right)\left( {s - b} \right)\left( {s - c} \right)} $, so use this concept to reach the solution of the question.

Complete step-by-step answer:
Given data-
The sides of the walls are 15m, 11m, and 6m, as shown in the given figure.
Now we have to find out the area painted in the green color.
Now as we see that the area painted in green color is in the shape of a triangle.
Let, a = 15m, b = 11m, and c = 6m.
Now as we know that if all the sides of the triangle are given then the area (A) of the triangle is given as,
$ \Rightarrow A = \sqrt {s\left( {s - a} \right)\left( {s - b} \right)\left( {s - c} \right)} $................. (1), where s is the half of the perimeter and a, b and c are the length of the sides of the triangle.
Now as we know that the perimeter is the sum of all the sides.
So, the perimeter of the triangle = a + b + c = 15 + 11 + 6 = 32m.
So, $s = \dfrac{{a + b + c}}{2} = \dfrac{{32}}{2} = 16$m
Now substitute all the values in equation (1) we have,
$ \Rightarrow A = \sqrt {16\left( {16 - 15} \right)\left( {16 - 11} \right)\left( {16 - 6} \right)} $
Now simplify this we have,
$ \Rightarrow A = \sqrt {16\left( 1 \right)\left( 5 \right)\left( {10} \right)} $
\[ \Rightarrow A = \sqrt {{4^2}\left( {{5^2}} \right)\left( 2 \right)} \]
\[ \Rightarrow A = 4\left( 5 \right)\sqrt {\left( 2 \right)} \]
\[ \Rightarrow A = 20\sqrt {\left( 2 \right)} \] Sq. m.
So this is the required area painted in green color.

Note: Whenever we face such types of questions the key concept we have to remember is that the perimeter of any shape is the sum of all the sides, so the perimeter of triangle is the sum of all the sides, so calculate it, so s is equal to half of the perimeter so calculate it then simply substitute the values in the area formula as above and simplify we will get the required answer.