Diagonals of a parallelogram are 8m and 6m respectively. If one side is 5m, then the area of Parallelogram is

a)18m2  b)30m2  c)24m2  d)48m2

Dear Student!

ABCD is a parallelogram. Let AC = 6 m and BD = 8 m

We know that, Diagonals of the parallelogram bisect each other.

In ΔOCD,

OC2 + OD2 = (3 m)2 + (4 m)2 = 9m2 + 16m2 = 25m2

CD2 = (5 m)2 = 25m2

∴ OC2 + OD2 = CD2

⇒ ΔOCD is a right triangle right angled at ∠O.

∴ ∠COD = 90°

In parallelogram ABCD, diagonals AC and BD bisect each other at 90°.

Hence, parallelogram ABCD is a rhombus.

∴ Area of parallelogram ABCD = × AC × BD = × 6m × 8m = 24 m2  

 (Area of Rhombus = Length of diagonal 1 × Length of diagonal 2)

Cheers!

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