Question

The perimeter of a trapezium is 52 cm. Its non-parallel sides are 10 cm each and the distance between two parallel sides is 8 cm. Find the area of the trapezium.

Answer 1

Hint: In this question, first work out on the perimeter of a trapezium by using P = sum of all sides of a trapezium. Second work out on the area of the trapezium by using $A=\dfrac{1}{2}\times \left( \text{Sum of parallel sides} \right)\times h$.

Complete step-by-step answer:
It is given that the perimeter of a trapezium is 52 cm, the distance between two parallel sides that mean the height of the trapezium is 8 cm and the distance between the non-parallel sides is 10 cm.

Form the above figure,
The perimeter of a trapezium = 10 + x + y +10
52 = 20 +x +y
x + y =52-20
x + y = 32
The sum of the parallel sides of a given trapezium is 32 cm.
The area of the given trapezium = $A=\dfrac{1}{2}\times \left( \text{Sum of parallel sides} \right)\times h$
Since h = 8 cm.
The area of the given trapezium = $A=\dfrac{1}{2}\times \left( 32 \right)\times 8$
The area of the given trapezium = $A=16\times 8$
The area of the given trapezium = $A=128$
Hence, the area of the given trapezium is 128$c{{m}^{2}}$.

Note: Alternatively, the question is solved as follow
Sum of length of parallel sides = perimeter-sum of non-parallel sides
                                                          = 52-20
                                                           =32
Area of trapezium = $\dfrac{1}{2}$ (The distance between parallel sides) (The sum of parallel sides)
                                   = $\dfrac{1}{2}\times 8\times 32$
                                   = $4\times 32$
                                  = 128
Area of trapezium=128 square cm.