Question

In the given figure, ABCD is a quadrilateral

then the area of quadrilateral

$ABCD$ = ___________________ $c{m}^2$

• A. 216
• B. 300
• C. 336
• D. 340

Answer 1

The correct option is C

336

$△ABD$

$S=\left(\frac{18+30+24}{2}\right)$

=$36cm$

$△=\sqrt{S(S-a)(S-b)(S-c)}$

=$\sqrt{36(36-24)(36-18)(36-30)}$

=$\sqrt{\left(36\right)\left(12\right)\left(18\right)\left(6\right)}$

=$\sqrt{6^2\times 6\times 2\times 18\times 6}$

=$\sqrt{6^2\times 6^2\times 6^2}$

=$216c{m}^2$

$△BDC$

$B{C}^2=D{C}^2-D{B}^2$

=${26}^2-{24}^2$

=${10}^2$

$BC=10cm$

$△DBC=\frac{1}{2}\times DB\times BC$

=$\frac{1}{2}\times 24\times 10$

=$120c{m}^2$

Area of quadrilateral $ABCD$

= $216+120$

= $336c{m}^2$