Question

All the vertices of a rhombus lie on a circle of radius R. If the length of one diagonal of the rhombus is D, then the area of the rhombus is:

• A. RD
• B. $\frac{RD}{2}$
• C. $\sqrt{2} \cdot RD$
• D. $\frac{\sqrt{2} \cdot RD}{2}$

Answer 1

Answer: (B)

$\frac{RD}{2}$

Answer 2

In a rhombus inscribed in a circle, the diagonals are equal in length and are diameters of the circle.
Therefore, the length of the other diagonal is also D.
$\text{Area of a rhombus} = \frac{\text{diagonal}_1 \times \text{diagonal}_2}{2}$

In this case, $\text{Area} = \frac{D \times D}{2} = \frac{D^2}{2}$

So, the area of the rhombus is $\frac{D^2}{2}$

Hence, the correct answer is (b) $\frac{RD}{2}$