Question

All the vertices of a rhombus lie on a circle. Find the area of the rhombus, if area of the circle is 2464 cm².

Answer 1

All  the vertices  of a rhombus lie  on a circle. So rhombus is a square.

Let the radius of a circle OA = OC = r & diagonals of a rhombus are d1 & d2, then
Diagonal of square (AC) = r + r = 2r

GIVEN:
Area of Circle = 2464 cm²

Area of Circle = πr²
2464 = πr²
2464 = π r²
r² = 2464 / π
r² = 2464 /(22/7)
r² = (2464 × 7)/22
r² = 112 × 7 = 784
r² = 784
r = √784 = √28×28 = 28

r = 28 cm

AC= 2r = 2×28 = 56 cm
AC = BD = 56 cm

[Diagonals of rhombus are equal]

Area of rhombus = ½(d1 × d2)
Area of rhombus = ½(56×56) = 28 × 56 = 1568 cm².

Hence, the Area of rhombus is 1568 cm².

HOPE THIS WILL HELP YOU...

Answer 2

hi! here is your answer !

refer to the pic.

The area of rhombus is 1568sq.cm.

hope this helps # ! ! !