Question

there is a sale in a park one of its side walls have been paint in some colour with a magazine in the park green and clean .if the side of the wall are 15m 11m and 6m find the area painted in colour

Answer 1

AnsweR :-

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.

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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.

Answer 2

Answer :-

• Area if painted wall = 20√2 cm²

Given :-

• Length of first side = 15 metres
• Length of second side = 11 metres
• Length of third side = 6 metres

To Find :-

• The area of Painted wall.

Explanation :-

As we know, by using Heron's Formulae we need semi-perimeter of triangle or triangular object.

Finding Semi-perimeter of wall

$\implies \rm \dfrac{Side \: 1 + Side \: 2 + Side \: 3}{2}$

$\implies \rm \dfrac{15 + 11 + 6}{2}$

$\implies \rm \dfrac{32}{2}$

$\blue { \boxed { \implies \rm \bold { 16 \: cm}}}$

Now, Substituting the values

$\implies \rm \sqrt{s (s - a) (s - b) (s - c)}$

$\implies \rm \sqrt{16 (16 - 15) (16 - 11) (16 - 6)}$

$\implies \rm \sqrt{16 (1) (5) (10)}$

$\implies \rm \sqrt{16 \times 1 \times 5 \times 10}$

$\implies \rm \sqrt{800}$

$\red { \underline { \boxed { \implies \rm { \bold { 20 \sqrt{2} \: cm^2 }}}}}</p><p>$

Hence, the area of painted wall is 20√2 cm²

@Agamsain