Question

ABCD is a parallelogram and O is the point of intersection of its diagonalsAC and BD. If the area of AAOD = 8cm, then find the area of parallelogram

Answer 1

Answer:

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