Question

The area of a trapezium is $ 34 c{m}^{2}$ and the length of one of the parallel sides is$ 10 cm$ and its height is$ 4 cm$ Find the length of the other parallel side.

10cm 

Answer 1

Finding the length of the other parallel side of the trapezium.

Let a trapezium $ABCD$ such that $AD\parallel BC$and $AB$ is the height.

Length of one parallel side, $BC=10cm$

height, $AB=4cm$and

Area of a trapezium is $34c{m}^2$

We know that,

Area of trapezium $=\frac{1}{2}\times \left(sumofparallelsides\right)\times height$

$$\begin{gathered} \Rightarrow Area=\frac{1}{2}\times \left(AD+BC\right)\times AB \\ \Rightarrow 34=\frac{1}{2}\times \left(AD+10\right)\times 4 \\ \Rightarrow 34=\left(AD+10\right)\times 2 \\ \Rightarrow 34=2AD+20 \\ \Rightarrow 34-20=2AD \\ \Rightarrow 2AD=14 \\ \Rightarrow AD=\frac{14}{2}=7cm \end{gathered}$$

Hence, another required parallel side is $7cm$