Question

ABCD is a rhombus with the diameters of a circle as its diagonals as shown in the figure below. What is the area of ABCD if the circumference of the circle is 44cm? (Use $\pi =\frac{22}{7}$)

• A. 44 ${\text{cm}}^2$
• B. 49 ${\text{cm}}^2$
• C. 98 ${\text{cm}}^2$
• D. 196 ${\text{cm}}^2$

Answer 1

The correct option is C 98 ${\text{cm}}^2$

Circumference of a circle = $\pi \times$diameter
$⟹$ Diameter = $\frac{\text{Circumference}}{\pi }$
= $\frac{44}{\pi }$ = 14 cm
As diameters of the circle are diagonals of the rhombus for the given figure,
$\text{area of rhombus}=\frac{1}{2}\times \text{product of diagonals}$

= $\frac{1}{2}\times (\text{diameter}{)}^2$
= $\frac{1}{2}\times {14}^2=98{\text{cm}}^2$