Multiple choice

A rhombus is formed by two radii and two chords of a circle whose radius is $16$cm. The area of the rhombus in sq.cm is.

  1. $128$
  2. $128\sqrt3$
  3. $256$
  4. $512$
  5. $512\sqrt3$
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B Correct answer
Explanation

A rhombus formed by two radii and two chords in a circle of radius R must have sides of length R. Since the radii form an angle at the center, the rhombus is composed of two equilateral triangles with side 16. Area = 2 * (sqrt(3)/4 * 16^2) = 128 * sqrt(3).

AI explanation

For two radii and two chords to form a rhombus, the chords must be equal in length and equidistant from the center, which geometrically confines the radii to form an angle of 60 degrees. The length of each side of the rhombus is equal to the circle's radius of 16 cm. Using the area formula for a rhombus, Area = side^2 * sin(angle), we find the area to be 16^2 * sin(60 degrees). Calculating this yields 256 * (sqrt(3) / 2), which equals 128*sqrt(3).

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