#### Question :

All the vertices of a rhombus lie on a circle. Find the area of rhombus,if the area of circle is 1256 cm²Submitted on 23/12/2023 | Answered by Vandana Rana#### Answer :

Given, all the vertices of a rhombus lie on a circle.Area of the circle = 1256 cm².

d

_{1}and d

_{2}are the diagonals of the rhombus.

```
Area of circle = πr²
```

1256 = 3.14r²

r² = 1256/3.14

r² = 400

r = 20 cm

Therefore, the radius of the circle is 20 cm. Since all the vertices of the rhombus lie on the circle. The diagonal of the rhombus is equal to the diameter of the circle.

```
Diameter of circle = 2(20) = 40 cm
```

Area of rhombus = 1/2 × d_{1} × d_{2}

= 1/2 × 40 × 40

= 20 × 40

= 800 cm²