Question

ABCD is a parallelogram and 'O' is the point of intersection of it's diagonals AC and BD. If the area of ∆AOD=8cm^2 the area of the parallelogram is ____.​

Answer 1

Given ABCD is a parallelogram and diagonals AC and BD intersect each other at O.  

So O is the midpoint of AC and BD.

Now, in △ADB  AO is  median  

 as median divides a triangle into two triangles of equal areas

Area(△ADB) = 2 Area(△AOD)

Area (△ADB) = 2×4 = 8 cm2    

△ADB and parallelogram ABCD have same base AB and lie between the parallel AB and CD.

 Area(ABCD) = 2 Area(△ADB)  

= 2×8  = 16 cm2  

Thus the area of parallelogram is 16cm^2

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