Q. 7

# In the given figu

Given: ABCD is a gm in which diagonals AC and BD intersect at O and ar(gm ABCD) is 52cm2.

Here,

Ar (∆ABD) = ar(∆ABC)

( ΔABD and ΔABC on same base AB and between same parallel lines AB and CD)

Here,

ar(∆ABD) = ar(∆ABC) = 1/2 × ar(||gm ABCD)

( ΔABD and ΔABC on same base AB and between same parallel lines AB and CD are half the area of the parallelogram)

ar(∆ABD) = ar(∆ABC) = 1/2 × 52 = 26cm2

Now, consider ΔABC

Here OB is the median of AC

( diagonals bisect each other in parallelogram)

ar(∆AOB) = ar(∆BOC)

(median of a triangle divides it into two triangles of equal area)

ar(∆AOB) = 1/2 × ar(ΔABC)

ar(∆AOB) = 1/2 × 26 = 13cm2

ar(∆AOB) = 13cm2

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