Question

Find the area of a trapezium whose parallel sides 25cm, 13cm and other sides are 15cm

and 15cm.

Answer 1

The area of Trapezium is 171 cm² .

Explanation:

Given as for a trapezium :

The measure of parallel sides are 25 cm and 13 cm

I.e AB = 25 cm , CD = 13 cm

The measure of other sides of the trapezium = AD = BC = 15 cm

Let The height of measure h is drawn on the side AB

So , The BOC is now a triangle

∴ The measure of BO = AB - AO = 25 cm - 13 cm = 12 cm

Let the area of Trapezium = A

Now, height h =
`\sqrt{BC^(2) - OB^(2)  }`

Or, h =
`\sqrt{15^(2) - 12^(2)  }`

Or, h =
`√(225 - 144  )`

∴ h =
`√(81)`

I.e h = 9 cm

From figure

∵ Area of trapezium =
`(1)/(2)`×Height×( sum of parallel side )

or, A =
`(1)/(2)`×h×( AB + CD )

or , A =
`(1)/(2)`×9×( 25 + 13 )

Or, A =
`(1)/(2)`×9×38

∴ Area = 171 cm²

Hence The area of Trapezium is 171 cm² . Answer