Question

parallel sides of a trapezium are 12 and 36 cm respectively.Its non parallel sides are each equal to 15 cm. Find area of trapezium?

Answer 1

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.

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

                                                        = 1/2 * (12+36) * 9

                                                        = 432/2

                                                        = 216 cm^2.


Hope this helps!

Answer 2

Answer: given below....

Step-by-step explanation: