Find the area of the shaded region in the figure.

see full answer

Start JEE / NEET / Foundation preparation at rupees 99/day !!

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

{cm}^{2}

384

{cm}^{2}

480

{cm}^{2}

None

answer is B.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

Area of a triangle is given by

\sqrt{s (s - a) (s - b) (s - c)}

.
Using the Pythagoras’s theorem in right angled triangle ADB, we get

{AB}^{2} = {AD}^{2} + {BD}^{2} = 16^{2} + 12^{2} = 256 + 144 = 400

\Rightarrow AB = 20

cm
Area of triangle ABD =

\frac{1}{2} \times AD \times BD = \frac{1}{2} \times 12 \times 16 = 96 {cm}^{2}

The perimeter of a triangle is the sum of the lengths of all the three sides.
The lengths of the three sides of the triangle ABC are 20 cm, 48 cm, and 52 cm.
Perimeter of triangle ABC=20+48+52=120 cm
s = 60 cm
Area of triangle ABC =

\sqrt{60 (60 - 20) (60 - 48) (60 - 52)} = \sqrt{60 \times 40 \times 12 \times 8} = 12 \times 8 \times 5 = 480 {cm}^{2}

⇒Area of shaded region=Area of triangle ABC - Area of triangle ABD
⇒Area of shaded region=480 - 96 = 384

{cm}^{2}

Watch 3-min video & get full concept clarity

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

How to Join IIT after 10th

🔥 Start Your JEE/NEET Prep at Just ₹1999 / month - Limited Offer! Check Now!

Get Expert Academic Guidance – Connect with a Counselor Today!

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

How to Join IIT after 10th