Question

What is the area of the quadrilateral shown below?

• A. $336c{m}^2$
• B. $460c{m}^2$
• C. $542c{m}^2$
• D. $606c{m}^2$

Answer 1

The correct option is A $336c{m}^2$

In $△BCD,$
$B{D}^2=B{C}^2+C{D}^2={12}^2+{16}^2=144+256$
$=400$
$BD=20cm$
$△ABD$ is an isosceles triangle, then the line AE bisect BD.
BE = 10 cm
In $△AEB,{26}^2=A{E}^2+{10}^2$
$A{E}^2={26}^2-{10}^2=676-100=576$
$AE=24cm$
Area of rectangle ABCD = Area of $△ABD+$ Area of $△BDC$
$=\frac{1}{2}\times 20\times 24+\frac{1}{2}\times 12\times 16=336c{m}^2$