Question

Find the area of the quadrilateral shown below:

Given: Area $\left(\Delta ADC\right)=16c{m}^2$

• A. $66c{m}^2$
• B. $76c{m}^2$
• C. $86c{m}^2$
• D. $96c{m}^2$

Answer 1

The correct option is B

$76c{m}^2$

Area $\left(\Delta ADC\right)=\frac{1}{2}\times \left(base\right)\times$ (corresponding height)

$16=\frac{1}{2}\times AC\times DE$

$16\times 2=AC\times 4$

$\Rightarrow AC=8cm.$

In Area of $\Delta ABC:a=15,b=17,c=8$

$s=\frac{a+b+c}{2}=\frac{17+15+8}{2}=\frac{40}{2}=20$

Area $=\sqrt{s(s-a)(s-b)(s-c)}$

$=\sqrt{20\times (20-15)\times (20-17)\times (20-8)}$

$=\sqrt{20\times 5\times 3\times 12}$

$=\sqrt{5\times 5\times 2\times 2\times 3\times 3\times 2\times 2}$

$=5\times 2\times 3\times 2=60c{m}^2$

$\therefore$ Area of quadrilateral ABCD $=60c{m}^2+16c{m}^2=76c{m}^2$