Abcd Is Parallelogram And O Is Point Of Intersection Of Its Diagonals

ABCD is a parallelogram and O is the point of intersection of its diagonals. If ar(ΔAOD) = 4 cm2, find area of parallelogram ABCD.

Answers:

Here, ABCD is a parallelogram in which its diagonals AC and BD intersect each other in O. 

∴  O is the mid – point of AC as well as BD.

Now, in △ADB , AO is its median 

∴ ar(△ADB) = 2 ar(△AOD) [∵ median divides a triangle into two triangles of equal areas]

So, (△ADB) = 2 × 4 = 8 cm²   

Now, △ADB and ||gm ABCD lie on the same base AB and lie between same parallel AB and CD .

∴ ar(ABCD) = 2 ar(△ADB) 

= 2 × 8 

= 16 cm²