Question

the area of a trapezium is 165 cm2 and its height is 10 cm. If one of the parallel sides is double of the other, find the two parallel sides.

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Answer 1

Answer:

Trapezium ABCD is divide into parallelogram AECD and triangle CEB. 

Now in △CEB, we have

EB=25−11=14cm

Using Heron’s theorem, we will first evaluate the semi-perimeter of △CEB and then evaluate its area.

S=2BE+EC+BC

⇒S=213+14+15=21cm

Therefore,

area of △CEB=S(S−BE)(S−EC)(S−BC)

⇒ Area of △CEB=21(21−13)(21−14)(21−15)=84cm2

As we know that,

Area of triangle =21× Base × height

Therefore,

Area of △CEB=21×14×BF

⇒BF=1484×2=12cm

Again, as we know that,

Area of trapezium = Sum of parallel sides × height

Therefore,

Area of trapezium ABCD=21×(11+25)×12=216cm2

Thus the area of trapezium is 216cm2.