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) = ?
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