Question

Calculate the area of the shaded region in the given figure.

• A. $1074m^2$
• B. $1274m^2$
• C. $1174m^2$
• D. $1004m^2$

Answer 1

The correct option is A $1074m^2$

For the triangle having the sides 122m, 120m and 22m :
$s=\frac{122+120+22}{2}=132m$
Area of triangle =$\sqrt{s(s-a)(s-b)(s-c)}$
$=\sqrt{132(132-122)(132-120)(132-22)}$
$=\sqrt{132\times 10\times 12\times 110}=1320m^2$
For the triangle having the sides 22m, 24m and 26m :
$s=\frac{22+24+26}{2}=36m$
$=\sqrt{36(36-22)(36-24)(36-26)}$
$=\sqrt{36\times 14\times 12\times 10}=24\sqrt{105}$
$=24\times 10.25m^2(approx.)=246m^2$
There, the area of the shaded portion
$=(1320-246)m^2=1074$ $m^2$