# CLASS-8PROBLEM & SOLUTION OF TRAPEZIUM

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.)