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Question

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

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Solution

Side of rhombus=20 cm.

One diagonal (d1)=24 cm

Diagonals of a rhombus bisect each other at right angle AB=20 cmand OA=12AC=12×24 cm=12 cm

In rightangled AOB,AB2=AO2+BO2 (Pythagoras theorem) (20)2=(12)2+BO2 400=144+BO2 BO2=400144=256=(16)2 BO=16 cmand diagonal BD=2×BO=2×16=32 cmNow area of rhombus ABCD=AC×BD2=24×322=24×16 cm2=384 cm2


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