Question

13. The area of an isosceles trapezium is 168 sq metres. If the lengths of the parallel
sides are 36 m and 20 m respectively, find the lengths of the non-parallel sides​

Answer 1

Given:

• Area of an isosceles trapezium is 168m²
• Length of parallel sides are 36m and 20m respectively.

To Find:

• Length of the non-parallel sides.

Solution:

Let ABCD be the isosceles trapezium with AC=20m and CO= 36m.

The area of the figure, (36-20)/2= 16/2= 8 m.

ABCD is 168 sq m.

Draw Of and BE perpendicular to CO from the vertices A and 8.

The area of the figure = (48+00)xh/2 =

168 [h = AF = BE ], or

(20+36 )×h = 2×168 = 336, or

h= 336/56 = 6m.

Now ADF and BCE are congruent right angle triangle, whose altitude is 6 m and the base=

(36-20)/2= 16/2 = 8m

The equal sides of the isosceles trapezium is

the same as the hypotenuse of ADF and BCF, which is [6² + 8² ]½= [ 36+64 ]½= 100½= 10m.

Hence, the length of the non-parallel sides will be 10m