Question

ABCD is a trapezium with parallel sides AB =a and DC = b. If E and F are mid-points of non-parallel sides AD and BC respectively, then the ratio of areas of quadrilaterals ABFE and EFCD is

(a) a : b

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

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

(d) (2a + b) : (3a + b)

Answer 1

Given: (1) ABCD is a trapezium, with parallel sides AB and DC

(2) AB = a cm

(3) DC = b cm

(4) E is the midpoint of non parallel sides AD.

(5) G is the midpoint of non parallel sides BC.

To find: Ratio of the area of the Quadrilaterals ABFE and EFCD.

Calculation: We know that, ‘Area of a trapezium is half the product of its height and the sum of the parallel sides.’

Since, E and F are mid points of AD and BC respectively, so h₁ = h₂

Area of trapezium ABFE

Now, Area (trap ABCD) = area (trap EFCD) + Area (ABFE)

Therefore,

Thus,

Hence, the correct option is (c)