Question

v's FORMULA
203
.
”
-- 6 m ------>
..
11 m -
KEEP THE PARK
GREEN AND CLEAN
15 m
Fig. 12.10
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.​

Answer 1

Given :-

The sides of the  wall are 15 m, 11 m and 6 m.

To Find :-

The area painted in colour.​

Analysis :-

Firstly, find the semi perimeter of triangular wall by it's respective formula and substitute their values.

Once you get the semi perimeter, find the area by the Heron's formula.

Solution :-

We know that,

• a = Area
• s = Semi perimeter

By the formula,

$\underline{\boxed{\sf Semi \ perimeter=\dfrac{a+b+c}{2} }}$

Given that,

The sides of the wall as 15 m, 11 m and 6 m.

Substituting their values,

$\sf =\dfrac{15+11+6}{2}$

$\sf = 16 \ m$

Therefore, the semi perimeter is 16 m.

By Heron's formula,

$\underline{\boxed{\sf Heron's \ formula=\sqrt{s(s-a)(s-b)(s-c)} }}$

Substituting their values,

$\sf =\sqrt{16(16-15)(16-11)(16-6)}$

$\sf = \sqrt{16 \times 1 \times 5 \times 10}$

$\sf =\sqrt{800}$

$\sf =20\sqrt{2}$

Therefore, the area painted in colour is 20√2 m².