Question

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

Answer 1

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Given,
Let ABCD be a rhombus of side 20 cm.

So, AB =BC= CD= AD = 20 cm [Sides of a rhombus are equal]

Let AC be the diagonal equal to 24 cm.

Therefore, AO = 12 cm.

IN AOD, APPLYING PYTHAGORAS THEOREM,

AD^2 = AO^2 + OD^2

=>400 = 144 + OD^2
=> OD^2 = 400 - 144
=> OD = 16.

So, BD = 2×16 = 32 cm

Now, Area of rhombus

= 1/2 × d1 × d2

= 1/2 × 24 × 32

= 12 × 32

= 384 cm^2

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Answer 2

Given, 
Let ABCD be a rhombus of side 20 cm.

So, AB =BC= CD= AD = 20 cm [Sides of a rhombus are equal]

Let AC be the diagonal equal to 24 cm.

Therefore, AO = 12 cm.

IN AOD, APPLYING PYTHAGORAS THEOREM,

AD^2 = AO^2 + OD^2

=>400 = 144 + OD^2
=> OD^2 = 400 - 144
=> OD = 16.

So, BD = 2×16 = 32 cm

Now, Area of rhombus

= 1/2 × d1 × d2

= 1/2 × 24 × 32

= 12 × 32

= 384 cm^2