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. 24cm^{2}

B. 40cm^{2}

C. 55cm^{2}

D. 27.5cm^{2}

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

BC^{2} = BM^{2} + MC^{2}

5^{2} = 4^{2} + MC^{2}

MC^{2} = 25—16

MC^{2} = 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 = = 40cm^{2}

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