Question

The perimeter of a trapezium is 52 cm and its non-parallel sides are each equal to 10 cm. If its altitude is 8 cm, what is its area?
(A). 128 $c{m^2}$
(B). 112 $c{m^2}$
(C). 118 $c{m^2}$
(D). 124 $c{m^2}$

Answer 1

Hint- Here, we have been given the perimeter of trapezium means the sum of all parallel and non-parallel sides is given. Also, we have been given non-parallel sides, so we can get the sum of parallel sides.

Complete step-by-step answer:

According to question,
Perimeter of trapezium= 52 cm, Height of trapezium= 8 cm
Sum of non-parallel sides=10+10 = 20 cm
$\therefore $ sum of parallel sides= Perimeter -Sum of non-parallel sides = 52-20 = 32 cm
Area of trapezium=$\dfrac{1}{2}\left( {Sum{\text{ }}of{\text{ }}parallel{\text{ }}sides} \right){\text{ }} \times {\text{ }}Height $
$\therefore $Area of trapezium= $\dfrac{1}{2}\left( {32} \right){\text{ }} \times {\text{ 8}}$
Hence, the area of trapezium is $128$ $c{m^2}$. Hence, option (A) is correct.

Note- For solving questions based on area, we have to see and find out the unknown, here the unknown is the sum of parallel sides. As perimeter is given and sum of non-parallel sides can be easily calculated from the given data. So, our mind should strike here to calculate the sum of parallel sides from the perimeter. Also, we need to remember the formula for the area of trapezium.