Q. 123.5( 2 Votes )

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

Answer :

Given:

Length of diagonal 1 (d_{1}) = 24 cm

Side = 20 cm

Let, Length of diagonal 2 be d_{2}

We know that,

Side of rhombus = 1/2 × √(d_{1}^{2} + d_{2}^{2} )

⇒ 20 = 1/2 × √(24^{2} + d_{2}^{2} )

⇒ 20 × 2 = √(576 + d_{2}^{2} )

⇒ 40 = √(576 + d_{2}^{2})

Squaring both sides,

⇒ 1600 = 576 + d_{2}^{2}

⇒ d_{2}^{2} = 1600-576

⇒ d_{2}^{2} = 1024

⇒ d_{2} = 32 cm

Now,

Area of rhombus= 1/2 × d_{1} × d_{2}

= 1/2 × 24 × 32

= 384 cm^{2}

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