All the vertices of a rhombus lie on a circle. Find the area of the rhombus, if area of the circle is `1256 cm^(2)` . (use `pi = 3.14`)

Explanation

Let the radius of the circle be r.
Given that, Area of the circle = `1256 cm^(2)`
`pir^(2) = 1256`
`rArr r^(2) = (1256)/(pi)=(1256)/(3.14)=400`
`rArr r^(2) = (20)^(2)`
`rArr` r = 20 cm
`:.` So, the radius of circle is 20 cm.
`rArr` Diameter of circle = `2xx` Radius
= `2xx20`
= 40cm
Since, all the vertices of a rhombus lie on a circle that means each diagonal of a rhombus must pass through the centre of a circle that is why both diagonais are equal and same as the diameter of the given circle.
Let `d_(1) and d_(2)` be the diagonals of the rhombus.
`:. d_(1)= d_(2)` = Diameter of circle = 40 cm
So, Area of rhombus = `(1)/(2)xxd_(1)xxd_(2)`
= `(1)/(2)xx40xx40`
= `20xx40 = 800 cm^(2)`
Hence, the required area of rhombus is `800cm^(2)`