ABCD is a trapezium with parallel sides $A B = a$ and $D C = b$ . 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 : b

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

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

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

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Solution

The correct option is C $(3 a + b) : (a + 3 b)$
Clearly, $E F = A B + \frac{D C}{2} = \frac{a + b}{2}$
Area of Trapezium = $\frac{1}{2}$ ( $S u m$ $o f$ $p a r a l l e l$ $s i d e s$ ) $\times h$
Let $h$ be the height as shown in figure, then
$a r (T r a p . A B F E) : a r (T r a p . E F C D)$
⇒ $\frac{1}{2} [a + \frac{a + b}{2}] \times h : \frac{1}{2} [b + \frac{a + b}{2}] \times h$
⇒ $\frac{2 a + a + b}{2} : \frac{2 b + a + b}{2}$
⇒ $3 a + b : a + 3 b$
Hence, this is the required ratio.

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Similar questions

Q. 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)

ABCD is a tapezium 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 quadrialaterals ABFE and EFCD is

Q. Question 10
ABCD is a trapezium with parallel sides. The ratio of ar (ABFE) and ar (EFCD) is:

A) a:b
B) (3a + b) : (a + 3b)
C) (a + 3b) : (3a + b)
D) (2a + b): (3a + b)

Q. 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, ar(ABFE) : ar(EFCD) = ?
(a) a : b
(b) (a + 3b) : (3a + b)
(c) (3a + b) : (a + 3b)
(d) (2a + b) : (3a + b)

A B C D

is a trapezium with parallel sides

A B = a

cm and

D C = b

cm.

E

and

F

are the mid-points of the non-parallel sides. The ratio of

ar (A B F E)

and

ar (E F C D)

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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:

The correct option is C (3a+b):(a+3b)Clearly, EF=AB+DC2=a+b2Area of Trapezium =12(Sum of parallel sides)×hLet h be the height as shown in figure, then ar(Trap.ABFE):ar(Trap.EFCD)⇒12[a+a+b2]×h:12[b+a+b2]×h⇒ 2a+a+b2:2b+a+b2⇒ 3a+b:a+3b Hence, this is the required ratio.

ABCD is a trapezium with parallel sides $A B = a$ and $D C = b$ . 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: