Question

1. Find the area of a trapezium whose parallel sides are 11 m and 25 m
long, and the nonparallel sides are 15 m and 13 m long.
​

Answer 1

Answer:

216 m2

Step-by-step explanation:

Draw DE∥BC and DL perpendicular to AB.

The opposite sides of quadrilateral DEBC are parallel.

Hence, DEBC is a parallelogram.

∴ DE = BC = 13 m  

Also,

AE=(AB-EB)=(AB-DC)=(25 - 11)=14 m

For ∆DAE:

Let:  

AE = a =14 m  

DE = b = 13 m

DA = c =15 m

Thus, we have:

s=a+b+c2s= 14+13+152=21 m

Area of ∆DAE =s(s-a)(s-b)(s-c)

=21×(21-14)×(21-13)×(21-15)

=21×7×8×6

=7056

=84 m2

Area of ∆DAE=12×AE×DL

⇒84=12×14×DL

⇒84×214=DL

⇒DL=12 m

Area of trapezium = 12×Sum of parallel sides × Distance between them

=12×(11+25)×12

=12×36×12

=216 m2