Question

find the area of shaded region​

Answer 1

$\bf\underline{\underline{\green{SOLUTION:-}}}$

Given

• AD= 12cm
• BD= 16cm
• AC = 52cm
• BC = 48cm

To Calculate

• Area of shaded region __?

Step by Step Explanation

In Tri. ABD

Where

AD = 12cm ( Given)

BD = 16cm ( Given)

AB = ?

By Pythagoras theorem

( hypotenuse) ² = ( Base ) ²+ ( Perpendicular) ²

➥ hypotenuse ² = 12²+16²

➥ hypotenuse ² = 144+256

➥ hypotenuse ²= 400

➥ hypotenuse = 20cm

Area of triangle ABD = 1/2×b×h

➥ 1/2 ×12×16

➥ 96cm²

Area of triangle ABC

Where

Sides are = 52cm,48cm,20cm

Semi Perimeter = (a+b+c)/2

➥( 52+20+48)/2

➥ 120/2

➥ 60cm

☆ By Heron's formula ☆

$Area \: of \: triangle = \sqrt{s(s - a)(s - b)(s - c)}$

Putting values,

$= \sqrt{60(60 - 52)(60 - 20)(60 - 48)}$

$= \sqrt{60 \times 8 \times 40 \times 12}$

$= \sqrt{30 \times 2 \times 4 \times 2 \times 2 \times 20 \times 4 \times 3}$

$= 2 \times 4 \sqrt{30 \times 2 \times 10 \times 2 \times 3}$

$= 2 \times 4 \times 2 \sqrt{30 \times 10 \times 3}$

$= 4 \times 2 \times 2 \sqrt{10 \times 3 \times 10 \times 3}$

$= 4 \times 2 \times 2 \times 10 \times 3$

$= 480cm ^{2}$

Area of triangle ABC = 4800cm²

Area of Shaded region = Area of triangle ABC - Area of triangle ABD

➥ 480-96

➥ 384cm²

$\bf\underline{\underline{\green{SOLUTION:-}}}$

• Area of Shaded region = 384cm²

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