The area of rhombus is

side

\times

side

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d_{1} \times d_{2}

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d_{1} + d_{2}

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\frac{d_{1} \times d_{2}}{2}

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Solution

The correct option is C $\frac{d_{1} \times d_{2}}{2}$
In rhombus $A B C D$ ,

$\Rightarrow A r e a (A B C D) = A (△ D A B) + A (△ B C D)$ ........ $(i)$

$\Rightarrow A (△ D A B) = \frac{1}{2} \times B D \times A O$ and

$\Rightarrow A (△ B C D) = \frac{1}{2} \times B D \times O C$

Let $A C = d_{1}, B D = d_{2}$

From $(i)$ ,

$\Rightarrow A (A B C D) = (\frac{1}{2} \times B D \times A O) + (\frac{1}{2} \times B D \times O C)$

$= \frac{1}{2} \times B D (A O + O C)$

$= \frac{1}{2} \times B D \times A C$

Hence, Area of rhombus $A B C D$ is $\frac{d_{1} \times d_{2}}{2}$ .

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