Question

The parallel sides of a Trapezium are 12 cm and 36 cm its non parallel sides are equal each begin 15 cm find the area of the trapezium​

Answer 1

Answer:

Explanation:

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

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.