Question

all the vertices of a rhombus lie on a circle. find the area of the rhombus, if area of the circle is 2464 cm square.

Answer 1

the ans is 392 the radius is 28 by using formula area of circle and area of rhombus

Answer 2

Answer:

$1568 cm^2$

Step-by-step explanation:

Area of circle = $\pi r^2$

We are given that area of the circle is 2464 cm square.

So, $2464=\pi r^2$

$2464=\frac{22}{7} \times r^2$

$\frac{2464}{\frac{22}{7} }= r^2$

$784= r^2$

$\sqrt{784}= r$

$28= r$

So, the radius of circle is 28 cm

Diameter = $2 \times r = 2 \times 28 = 56 cm$

Since, all the vertices of a rhombus lie on a circle that means each diagonal of a rhombus pass through the centre of a circle So, both diagonals are equal and same as the diameter of circle.

Area of rhombus=$\frac{\text{Product of diagonals}}{2}$

                          =$\frac{56 \times 56}{2}$

                          =$1568 cm^2$

Hence the area of the rhombus is $1568 cm^2$