Question

ABCD is a trapezium with parallel sides AB = a cm , CD = b cm. E and F are the mid points of the non-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 )

Pls. show how you solved this ques, through steps

Answer 1

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Answer 2

The ratio of trapezium is b) (3a + b) :(a + 3b)

Since E and F are mid points of AD and BC.

Therefore, EF will be parallel to both AB and CD, thus -

EF = a+b/2

ABFE and CDEF both are trapezium., where ABFE is a trapezium with parallel sides AB and EF which are 'a' and a+b/2.

Thus,

Area ( ABFE) = 1/2 ( a+ a+b/2)/2, where h' is the height of trapezium

Area ( CDEF) = 1/2 ( b+ a+b/2)/2, where h'' is the height of trapezium

Since E is mid point of side AD and EF || AB

Therefore, EY must be the height of trapezium  = h' = h''

Hence,

Area ( ABFE) = 1/2 ( a+ a+b/2)/2/ Area ( CDEF) = 1/2 ( b+ a+b/2)/2

= 3a +b/ a+3b

Thus, the ratio of ar(ABFE) and ar(EFCD) is: (3a + b) :(a + 3b)