Question

find the area of shaded region ​

Answer 1

Step-by-step explanation:

Find AB using Pythagoras theroum

Then find the area of the big triangle (ABC) using herons formula

Find the area of the small triangle (ABD) using half x base height

area of ABC - Area of ABD is the area of shaded region.

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Answer 2

Answer:

$384 \: {cm}^{2}$

Solution:-

Triangle ABD is right angled triangle

By Pythagoras theorem

AB^2+BD^2=AB^2

12^2+16^2=AB^2

144+256=AB^2

400=AB^2

AB=20 cm

Now in triangle ABC

AB^2+BC^2

20^2+48^2

400+2304

2704

(52)^2

52 cm which is equal to AC

Hence triangle ABC is right angled triangle

Now

Area of shaded portion=Area of triangle ABC-Area of triangle ABD

$= \frac{1}{2} \times bc \times ad - \frac{1}{2} \times ad \times bd$

$= \frac{1}{2} \times 20 \times 48 - \frac{1}{2} \times 12 \times 16$

$= 480 - 96$

$= 384 \: {cm}^{2}$

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Area of shaded portion=384 cm^2