Question

In fig. Seg $AD$ $\parallel$ Seg $DC$ and Seg $DA$ $\perp$ Seg $AB$. Further $DC=7$ cm, $CB=10$ cm and $AB=13$ cm. Find the area of $\square ABCD$.

• A. $160c{m}^2$
• B. $100|:c{m}^2$
• C. $50c{m}^2$
• D. $80c{m}^2$

Answer 1

The correct option is D $80c{m}^2$

Area of quadrilateral $ABCD=$ area of rectangle $AECD+$ area of $△$ $BEC$.
Now, $AE=DC$ and $AD=EC$
$\therefore AB=AE+EB$
$\Rightarrow 13=DC+EB$
$\Rightarrow 13=7+EB$
$\Rightarrow EB=6$ cm
$△BEC$ is a right angle triangle.
Therefore, $B{C}^2=B{E}^2+E{C}^2$
$\Rightarrow {10}^2=6^2+E{C}^2$
$\Rightarrow E{C}^2=100-36$
$\Rightarrow E{C}^2=64$
$\Rightarrow EC=8$ cm
Now, $△BEC=\frac{1}{2}\times BE\times EC$
$=\frac{1}{2}\times 6\times 8$
$=24c{m}^2$
Area of rectangle $AECD=AE\times CE$
$=7\times 8$
$=56c{m}^2$
Area of quadrilateral $ABCD$ $=56+24$ $=80c{m}^2$