In the given figure,ABCD is a ||gm in which diagonals AC and BD intersect at O.If ar(||gm ABCD) is 52 $c m^{2}$ then the ar $(△ A O B)$ =?

(a) $26 c m^{2}$

(b) $18.5 c m^{2}$

(c) $39 c m^{2}$

(d) $13 c m^{2}$

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Solution

(d) $13 c m^{2}$
The diagonals of a parallelogram divides it into four triangles of equal areas.
∴ Area of ∆OAB = ⨯ ar(||gm ABCD)
⇒ ar(∆OAB) = ⨯ 52 = $13 c m^{2}$

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