Question

12. Find the area of a rhombus each side of which measures 20 cm and one of whose diagonals
is 24 cm.​

Answer 1

Answer:

AO=OC=CB=BA=20cm−[side of rhombus]

AC=24cm

AO=

2

1

×AC=

2

1

×24=12cm−[originals of rhombus bisect each other]

∴ In right angled triangle AOD,

AD

2

=AO

2

+OD

2

−By Pythagoras theorem

(20)

2

=(12)

2

+OD

2

∴OD

2

=400−144

∴OD=

256

∴OD=16cm

∴OB=2×16=32cm

∴ Area of rhombus=

2

1

× product of diagonals

=

2

1

×32×24=384cm

2