Multiple choice

All the vertices of a rhombus lie on a circle., if area of the circle is 1256 $cm^2 .$ (Use $\pi =$ 3.14), then find out the area of the rhombus?

  1. $1600 cm^2$
  2. $800 cm^2$
  3. $400 cm^2$
  4.  $200cm^2$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Area of circle = pi * r^2 = 1256. r^2 = 1256 / 3.14 = 400, so r = 20. The rhombus vertices lie on the circle, meaning the diagonals of the rhombus are diameters of the circle (d1 = d2 = 40). Area of rhombus = 1/2 * d1 * d2 = 1/2 * 40 * 40 = 800.

AI explanation

The area of the circle is pi times radius squared, so 3.14 times radius squared equals 1256, giving a radius of 20 cm. The diameter of the circle is 40 cm, which becomes the diagonal of the inscribed rhombus. Since all vertices lie on the circle, it forms a square with diagonals of 40 cm, and the area of a rhombus is half the product of its diagonals, giving 0.5 times 40 times 40, which equals 800 cm squared.

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