Question

The parallel sides of the trapezium are of length 60 units and 100 units and non parallel sides are of length 20 units and 30 units. If the area of trapezium is 100a√15 unit², then find the value of
a.​

Answer 1

Given:

The length of the parallel sides of the trapezium = 60 units and 100 units.

The length of non-parallel sides = 20 units and 30 units

Area of the trapezium = 100a√15 unit²

To find:

The value of a.

Solution:

Using Pythagoras Theorem we get:

x² + h² = 20².......equation 1

x² + h² = 400

(40-x)² + h² = 30²....... equation 2

1600 + x² - 80x + h² = 900

1600 + 400 -80x = 900

1100 = 80x

x = 55/4 = 13.75 units

h = 14.5 units

Area of trapezium = 1/2 (sum of parallel sides)*height

= 1/2 *(60 + 100)* 14.5

=725 sq. units

Therefore the area of trapezium is 725 sq. units.