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

Options

A. `24 cm^(2)`
B. `40 cm^(2)`
C. `55 cm^(2)`
D. `27.5 cm^(2)`

Answer

B

Explanation

`CM^(2)=BC^(2)-BM^(2)=(5)^(2)-(4)^(2)=9 rArrCM=3 cm.`
Similarly, DL = 3 cm.
`therefore CD = DL + LM + CM =(3+7+3)cm = 13 cm.`
ar(trap. ABCD) `=[(1)/(2)xx(7+13)xx4]cm^(2)=40 cm^(2)`.