Example.1) The parallel sides of a trapezium are 8 cm and 12 cm. if its area is 150 cm², then find the height of the trapezium.
Ans.) let the height of the trapezium = a cm, as per the given condition the parallel sides of trapezium is 8 cm and 12 cm, area = 150 cm²
As we know that the area of the trapezium -
1
= ------- X (sum of its parallel sides) X height
2 1
150 cm² = ------- X (8 cm + 12 cm) X a
2
20 cm X a = 150 cm² X 2
a = 15 cm
so, the height of the trapezium is 15 cm (Ans.)
Example.2) The two parallel sides of a trapezium are in the ratio 5 : 7 and the distance between them is 11 cm. if the area of the trapezium is 396 cm², find the length of the parallel sides
Ans.) Let the lengths of the two parallel sides of the trapezium be 5x cm & 7x cm
As we know area of the trapezium -
1
= ------ X (sum of its parallel sides) X height
2
1
Or, 396 = ------- X (5x + 7x) X 11
2
396 X 2
Or, 12x = ------------ = 72
11
Or, x = 72/12 = 6 cm
Thus the length of the sides are = 5x = 5 X 6
= 30 cm and 7x = 7 X 6 = 42 cm
So, the obtained sides of the trapezium are 30 cm & 42 cm. (Ans.)