Multiple choice

Rectangle ABCD is inscribed in a circle If AB = 12 cm and BC = 5 cm Find the area of the shaded part (use $\displaystyle \pi =3.14 $)

  1. 72.665 $\displaystyle cm^{2} $
  2. 72 $\displaystyle cm^{2} $
  3. 72.165 $\displaystyle cm^{2} $

  4. None of these
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AI explanation

Since the rectangle is inscribed in the circle, its diagonal forms the diameter of the circle; using the Pythagorean theorem on sides 12 cm and 5 cm yields a diagonal of 13 cm. The radius of the circle is therefore 6.5 cm, making the total area of the circle 3.14 times 6.5 squared, which is 132.665 square cm. The area of the rectangle is 12 times 5, equaling 60 square cm. Subtracting the rectangle's area from the circle's area leaves a shaded area of 132.665 minus 60, which is 72.665 square cm.

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