Find the area of the rhombus in which each side is 25 cm long and one of whose diagonals is 14 cm.
Answer:
336 cm2
- Let ABCD be the given rhombus with
AB=25 cm and AC=14 cm.
Let the diagonals AC and BD bisect at a point O.
We know that the diagonals of a rhombus bisect each other at right angles.
So, AO=12AC and BO=12BD. ∴AO=12×14=7 cm and ∠AOB=90∘ - Using Pythagous' theorem in right △AOB, we have AB2=AO2+BO2⟹(25)2=(7)2+BO2⟹625=49+BO2⟹576=BO2⟹24 cm=BO As, BO=12BD, we have BO=12BD⟹24=12BD⟹2×24=BD⟹48 cm=BD
- We know, Area of rhombus =12× Product of its diagonals =12×AC×BD=12×14×48 cm=336 cm2 Thus, the area of the rhombus is 336 cm2.