All the vertices of a rhombus lie on a circle. Find the area of the rhombus, if area of the circle is 1256 cm2. (use π = 3.14)


Are of the circle = 1256 cm2


Let r be the radius of the circle.


Area = πr2 1256 = 3.14 × r2 r2 = 1256/3.14 = 400


r = 20 cm


Diameter of the circle = d = 2×20 = 40 cm


Since all the vertices of a rhombus lie on a circle, therefore the diagonals of the rhombus pass through the center of the circle and thus diagonals of the rhombus are equal to the diameter of the circle.


Let d1 and d2 be the diagonal of the rhombus.


Since, diagonals of a rhombus are equal, therefore d1 = d2 = d = 40 cm


Now, Area of the rhombus = (1/2) × d1 × d2


= (1/2) × 40 × 40 = 800 cm2


Hence, the required area of rhombus is 800 cm2.


12
1