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Area of Rhombus

Find the area...

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 $(d_{1})$ =24 cm

$∴ D i a g o n a l s o f a r h o m b u s b i s e c t e a c h o t h e r a t r i g h t a n g l e A B = 20 c m a n d O A = \frac{1}{2} A C = \frac{1}{2} \times 24 c m = 12 c m$

$I n r i g h t - a n g l e d △ A O B, A B^{2} = A O^{2} + B O^{2} (P y t h a g o r a s t h e o r e m) \Rightarrow (20)^{2} = (12)^{2} + B O^{2} \Rightarrow 400 = 144 + B O^{2} \Rightarrow B O^{2} = 400 - 144 = 256 = (16)^{2} ∴ B O = 16 c m a n d d i a g o n a l B D = 2 \times B O = 2 \times 16 = 32 c m N o w a r e a o f r h o m b u s A B C D = \frac{A C \times B D}{2} = \frac{24 \times 32}{2} = 24 \times 16 c m^{2} = 384 c m^{2}$

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