Question

there is a slide in the park . one of its side walls has been painted in some colour with a message " keep the park clean " if th sides of the wall are 15m,11m,and 6m , find the area painted in colour

Answer 1

Given : The side of the Triangles are 11 metres 6 metres and 15meters

To find: The area painted in colour

Sol : The perimeter of the triangle = sum of three sides

⟹ 11m + 6m + 15m

= 32m

Now

The semiperimeter of triangle = 32/ 2

= 16 meters

By using Heron's formula

The area painted in colour =

$\sqrt{16 (16 - 11)(16 - 15)(16 - 6)} \\ ⟹ \: \sqrt{16 \times 5 \times 1 \times 10} \\ ⟹ \sqrt{80 \times 10} \\ ⟹ \sqrt{800} \\ ⟹ \sqrt{(2 \times 2) \times( 2 \times 2) \times 2 \times( 5 \times 5)} \\ ⟹2 \times 2 \times 5 \sqrt{2 } \\ ⟹ \underline{ \underline\bold{20 \sqrt{2} }}$

Answer 2

Given :-

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

To Find :-

• Find the area painted in color ?

Solution :-

we know that, area of a ∆ with sides as a, b and c is ,

• Area = √[s*(s - a)(s - b)(s - c)] where s is semi - perimeter.
• s = (a + b + c)/2 .

so,

→ s = (15 + 11 + 6)/2

→ s = 32/2 = 16 cm.

then,

→ Area of ∆ = √[16 * (16 - 15) * (16 - 11) * (16 - 6)]

→ Area = √[16 * 1 * 5 * 10]

→ Area = √(4² * 5² * 2)

→ Area = 4 * 5√2

→ Area = 20√2 m². (Ans.)

Learn more :-

In ABC, AD is angle bisector,

angle BAC = 111 and AB+BD=AC find the value of angle ACB=?

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