Question

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

• A. 72.665 $c{m}^2$
• B. 72 $c{m}^2$
• C. 72.165 $c{m}^2$
• D. None of these

Answer 1

The correct option is A 72.665 $c{m}^2$

Given $ABCD$ is a rectangle inscribed in a circle.

$AB=12cm$ and $BC=5cm$

Area of rectangle $ABCD=AB\ast BC=12\ast 5=60c{m}^2$

In rectangle ABCD; $\angle ABC={90}^o$

According to Central Angle Theorem; $\angle AOC={180}^o$

It means AC is diameter of circle and also hypotenuse of right triangle ABC.

Using Pythagoras Theorem in right triangle ABC;

$A{C}^2=A{B}^2+B{C}^2={12}^2+5^2=144+25=169$

$AC=\sqrt[2]{2169}=13cm$

$Diameter,AC=13cm$

Area of circle $=\pi r^2=3.14\ast {\left(\frac{AC}{2}\right)}^2=\frac{3.14\ast {AC}^2}{4}=\frac{3.14\ast {\left(13\right)}^2}{4}=\frac{3.14\ast 169}{4}=132.665c{m}^2$

Area of shaded region $=$ Area of circle $-$ Area of rectangle $=132.665-60=72.665c{m}^2$