Question

The perimeter of a trapezium is $52cm$ and its each non parallel side is equal to $10cm$ with its height $8cm.$Its area is

• A. $124c{m}^2$
• B. $118c{m}^2$
• C. $128c{m}^2$
• D. $112c{m}^2$

Answer 1

The correct option is C

$128c{m}^2$

Let the parallel sides of the trapezium be $a$and $b.$

Given , non parallel sides are $10cm$each and Perimeter of trapezium $52cm.$

According to question ,

$$\begin{gathered} a+b+10+10=52 \\ a+b+20=52 \\ a+b=52-20 \\ a+b=32 \end{gathered}$$

Area of trapezium = $\frac{1}{2}\times \left(\mathrm{Sum}\mathrm{of}\mathrm{parallel}\mathrm{sides}\right)\times \mathrm{Distance}\mathrm{between}\mathrm{them}$

=$\frac{1}{2}\times \left(a+b\right)\times 8$

= $\frac{1}{2}\times 32\times 8$

= $16\times 8=128c{m}^2$

Hence , area of trapezium is $128c{m}^2.$