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In the given figure ABCD is a trapezium in which AB || DC such that AB = a cm and DC = b cm. If E and F are the midpoints of AD and BC respectively. Then, the ratio of area of trapezium ABFE to area of trapezium EFCD is:

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a: b

(a + 3b): (3a + b)

(3a + b): (a + 3b)

1: 1

answer is C.

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Detailed Solution

Given a trapezium ABCD.
In the given figure, ABCD is a trapezium in which AB||DC such that AB = a cm and DC = b cm. If E and F are the midpoints of AB and

Let the distance between parallel sides = d cm.
By using mid-point theorem,
EF =

A B + D C 2

EF =

a + b 2

Area of trapezium ABEF is,

A = 12 × a + b 2 + a × d A = 12 × a + b + 2 a 2 × d A = 12 × 3 a + b 2 × d

Area of trapezium EFCD is,

A = 12 × b + a + b 2 × d A = 12 × a + b + 2 b 2 × d A = 12 × a + 3 b 2 × d

Now, the ratio is

R a t i o = 12 × 3 a + b 2 × d 12 × a + 3 b 2 × d R a t i o = 3 a + b a + 3 b

Ratio of area of trapezium ABFE to area of trapezium EFCD is (3a + b): (a + 3b).
Hence, option 3 is correct.

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