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!