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In the given figure, ABCD is a parallelogram in which diagonals AC and BD intersect at O. If area of parallelogram ABCD is 52 $c m 2$ , then the area of triangle OAB is ____ $c m 2$ .

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Detailed Solution

In the given figure, ABCD is a parallelogram in which diagonals AC and BD intersect at O. If area of parallelogram ABCD is 52

c m 2

, then the area of triangle OAB is 13

c m 2

.
Given a parallelogram ABCD having area 52

c m 2

.
Since, diagonal of parallelogram bisects each other and diagonal divide parallelogram into 2 triangles having equal area.
Therefore, area of triangle ABCD =

12 ×

area of triangle ABC

A = 12 × 52 A = 26 c m 2

Now, as OB is median of triangle ABC.
area of triangle OAB =

12 ×

area of triangle ABC

A = 12 × 26 A = 13 c m 2

Area of triangle OAB is 13

c m 2

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