Math, asked by Snehal72007, 7 months ago

Find the distance between the two parallel sides of a trapezium whose parallel sides are 36m and 12m and non parallel sides are 15m each.

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Answers

Answered by ashauthiras
2

Answer

Step-by-step explanation:

Let ABCD be the trapezium & AB = 36 cm, DC = 12 cm and AD = 12cm.

Now, EB = (AB-AE) = (AB-DC)

= 36 - 12

= 24cm.

In triangle EBC, CE = BC = 15cm.

CF is perpendicular to AB.

F is the midpoint of EB.

EF = 1/2 * AB

= 1/2 * EB

= 1/2 * 24

= 12cm.

In right- angled triangle CFE, CF = 15cm, EF = 12cm.

By Pythagoras theorem, we have

CF = root CE^2 - EF^2

= (15^2 - 12^2)

= root 225 - 144

= root 81

= 9.

The distance between the parallel sides = 9cm.

∴ , Area of the trapezium = 1/2 * (sum of parallel sides) * (distance)

  = 1/2 * (12+36) * 9

= 432/2

= 216 cm^2.

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