Question

If the lengths of the diagonals of a rhombus are 16 cm and 12 cm, find its area.​

Answer 1

Answer:

⇒ Let ABCD be the rhombus and AC and BD bisect at point O. AC = 16cm and BD = 12cm.

⇒ We know that the diagonals of rhombus bisect at right angles.

⇒ AO=

2

16

=8cm

⇒ BO=

2

12

=6cm

⇒ In right angled △AOB,

By using Pythagoras theorem,

⇒ AB

2

=AO

2

+BO

2

⇒ AB

2

=8

2

+6

2

⇒ AB

2

=64+36

⇒ AB

2

=100

⇒ AB=

100

⇒ AB=10cm

∴ Side of a rhombus is 10cm.

Answer 2

Area of rhombus=1/2x1st diagonal x 2nd diagonal

                           =1/2 x 16 x 12

                           =16 x 6

                           =96