In trapezium ABCD, parallel sides AB=a cm and DC = b cm. E & F are the mid points of sides AD & BC respectively. Find the ratio of ar(ABFE) to the ar(EFCD).
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Clearly, EF = AB + DC / 2 = a + b / 2
Let h be the height , then
ar(Trap. ABFE) : ar(Trap. EFCD)
⇒ 1/2 [a + (a+b / 2)] × h : 1/2 [b + (a+b / 2)] × h
⇒ 2a + a + b / 2 : 2b + a + b / 2
⇒ 3a + b : 3b + a
Let h be the height , then
ar(Trap. ABFE) : ar(Trap. EFCD)
⇒ 1/2 [a + (a+b / 2)] × h : 1/2 [b + (a+b / 2)] × h
⇒ 2a + a + b / 2 : 2b + a + b / 2
⇒ 3a + b : 3b + a
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