Question

Find the area of a rhombus if the length of its side 20 is cm and one of its diagonals is 24 cm. The area of the rhombus is ____________ Sq.cm.[Using Pythagoras theorem find other diagonal]

Answer 1

Answer:

Find Area of Rhombus

Side = 20 cm

one diagonal is 24 cm

→□ABCD BC = 24 cm, so, BM=MC=

2

24

=12cm

→ diagonals AD=AM+MD

→In△AMC, using Pythagoras theorem

AC

2

=AM

2

+MC

2

(20)

2

=AM

2

+(12)

2

AM

2

=(20)

2

+(12)

2

=400−144

AM

2

=256

AM=

256

AM=16cm

→AM=MD=16cm

→ Area of Rhombus =

2

1

× Product of diagonal

=

2

1

×(AD.BC)

=

2

1

×((16+16).24)

=

2

1

×32×24

=384cm

2