Question

Find the area of the shaded region in Fig.

• A. $384$ sq cm
• B. $480$ sqcm
• C. $96$ sqcm
• D. none

Answer 1

The correct option is A $384$ sq cm

In $△ADB$, Using Pythagoras Theorem

$AB=\sqrt{A{D}^2+B{D}^2}=\sqrt{{12}^2+{16}^2}=\sqrt{144+256}=\sqrt{400}=20cm$

$ar△ABD=\frac{1}{2}\times BD\times AD=\frac{1}{2}\times 16\times 12=96c{m}^2$

$ar△ABC$ $=\sqrt{S(S-a)(S-b)(S-c)},S=\frac{48+52+20}{2}=60cm=\sqrt{60(60-48)(60-52)(60-20)}=\sqrt{60\times 12\times 8\times 40}=480c{m}^2$

Hence, Required Shaded Area $=480-96=384c{m}^2$