Question

The parallel side of a trapezium is 6cm and 14cm. The non parallel sides are 5cm. Find its area

Answer 1

Hey Friend,

It is given that the non-parallel sides are 5 cm. So, both are equal...therefore, the trapezium is an isosceles trapezium.

Refer to the diagram in the attachment...

So, DC = OP = 6 cm

therefore, AO + BP = 14 - 6 = 8 cm

since, ABCD is an isosceles trapezium, 
AO = BP
AO = 8/2 = 4 cm

Applying Pythagoras Theorem,
In triangle AOD,

AD^2 = AO^2 + DO^2
5^2 - 4^2 = DO^2
DO^2 = 25 - 16
DO = $\sqrt{9}$
DO = 3 cm

Now, Area of a trapezium = (AB + CD) DO / 2
                                         = 3 (6+14) / 2
                                         = 3 x 20 / 2
                                         = 30 cm^2

Therefore, the area of trapezium is 30 cm^2

Hope it helps!