Q. 125.0( 1 Vote )

In the given figure ABCD is a trapezium such that AL DC and BM DC. If AB = 7cm, BC = AD = 5cm and AL = BM = 4cm, then ar(trap. ABCD) = ?


A. 24cm2

B. 40cm2

C. 55cm2

D. 27.5cm2

Answer :

Given:


AL DC


BM DC


AB = 7cm


BC = AD = 5cm


AL = BM = 4cm


Here,


MC = DL and AB = LM = 7 cm


Consider the ΔBMC


Here, by Pythagoras theorem


BC2 = BM2 + MC2


52 = 42 + MC2


MC2 = 25—16


MC2 = 9


MC = 3cm


MC = DL = 3cm


CD = DL + LM + MC = 3 + 7 + 3 = 13cm


Now,


Area of the trapezium is given by:


Area of the rhombus = = 40cm2

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