Question

Find the area of the parallelogram in which $AD=5cm,DE=3cm$ and $AB=10cm$. [$AE$ is the height of the parallelogram]

• A. $15c{m}^2$
• B. $50c{m}^2$
• C. $30c{m}^2$
• D. $40c{m}^2$

Answer 1

The correct option is D

$40c{m}^2$

Since, $AE$ is the height of the parallelogram, so, $AE$ is perpendicular to $CD$.

$\Rightarrow △ADE$ is a right angled triangle, right angled at $E$.

Applying Pythagoras Theorem in $△ADE$:

$A{D}^2=A{E}^2+D{E}^2$

$\Rightarrow A{E}^2=A{D}^2-D{E}^2=5^2-3^2=16$

$\Rightarrow AE=4cm$

Now, in parallelogram $ABCD,AB=10cm\Rightarrow CD=10cm$ [Opposite sides are parallel and equal in a parallelogram]

Area of parallelogram $ABCD=$ Base $\times$ Height

Base $=CD=10cm$

Height $=AE=4cm$

$\Rightarrow$ Area $=CD\times AE=10\times 4=40c{m}^2$