Question : The perimeter of a rhombus is 100 cm and one of its diagonals is 40 cm. Find its area.
Option 1: 1200 cm2
Option 2: 1000 cm2
Option 3: 600 cm2
Option 4: 500 cm2
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Correct Answer: 600 cm 2
Solution :
The perimeter of a rhombus is $\operatorname{100 cm}$.
The side of the rhombus = $\frac{100}{4}=\operatorname{25 cm}$.
Given that one of its diagonals is $\operatorname{40 cm}$.
Let another diagonal be $d_2$.
$⇒d_2 = 2 \sqrt{(25)^2 - (20)^2} = 30 \text{ cm}$
The area of a rhombus, where $d_1$ and $d_2$ are the diagonals.
$=\frac{1}{2} \times d_1\times d_2$
$= \frac{1}{2} \times 40 \times 30 = 600 \text{ cm}^2$
Hence, the correct answer is 600 cm
2
.
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