Question

message
There is a slide in a park. One of its side walls has been painted in some colour with a
"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.
6 m
11 m
KEEP THE PARK
GREEN AND CLEAN
15 m​

Answer 1

The perimeter of a triangle is equal to the sum of its three sides it is denoted by 2S.

2s=(a+b+c)

s=(a+b+c)/2

Here ,s is called semi perimeter of a triangle.

The formula given by Heron about the area of a triangle is known as Heron's formula.

According to this formula area of a triangle= √s (s-a) (s-b) (s-c)

Where a, b and c are three sides of a triangle and s is a semi perimeter.

This formula can be used for any triangle to calculate its area and it is very useful when it is not possible to find the height of the triangle easily .

Heron's formula is generally used for calculating area of scalene triangle.

___________________

_________________

Solution:

Here area painted in colour will be equal to the area of triangle with side 15m,11m and 6 m

Let the Sides of the triangular wall are a=15 m, b=11 m & c=6 m.

Semi Perimeter of the ∆,s = (a+b+c) /2

Semi perimeter of triangular wall (s) = (15 + 11 + 6)/2 m = 16 m

Using heron’s formula,

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

= √16(16 – 15) (16 – 11) (16 – 6)

= √16 × 1 × 5 × 10

= √ 4×4×5×5×2

= 4×5√2

= 20√2 m²

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

=========================================

Hope this will help you...

Answer 2

$\sf{\huge{\underline{\red{Given :-}}}}$

• There is a slide in a park.

• Its side walls has been painted in some colour with a"KEEP THE PARK GREEN AND CLEAN”.

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

$\sf{\huge{\underline{\green{To\:Find :-}}}}$

• The area to painted in colour.

$\sf{\huge{\underline{\orange{Solution :-}}}}$

Area to be painted in colour = Area of the triangle

We have,

• a = 15 m

• b = 6 m

• c = 11 m

Finding 's' .We know,

S = $\dfrac{a + b + c}{2}$

➝ S = $\dfrac{15 + 6 + 11}{2}$

➝ S = $\cancel{\dfrac{32}{2}}$

➝ S = 16

Using Herons formulae,

$\sqrt{s(s - a)(s - b)(s - c)}$ m²

Now put value from above ,

➝ $\sqrt{16(16 - 15)(16 - 6)(16 - 11)}$ m²

➝ $\sqrt{16 \times 1 \times 5 \times 10} \: m {}^{2}$

➝ √16 × √5 × √10 m²

➝ √16 × √5 × 10 m²

➝ √4 × 4 × √5 × 5 × 2 m²

➝ 4 × 5 × √2 m²

➝ 20√2 m²

Hence, The area to painted in colour is 20√2 m².

____________________________________