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  • In Figure 5, ABCD is a square with side  cm and inscribed in a circle. Find the area of the shaded region. (Use <img alt="\pi" src="https://entrancecor

In Figure 5, ABCD is a square with side 2\sqrt{2} cm and inscribed in a circle. Find the area of the shaded region. (Use \pi = 3·14)

 

 

 

 
 
 
 
 

Answers (1)

ABCD Square with side 2\sqrt2cm

Diameter of circle = AC = \sqrt{(2\sqrt2)^2 + (2\sqrt2)^2}

AC = \sqrt{16} = 4 cm

Radius of circle = \frac{AC}{2} = \frac{4}{2} = 2 cm

\begin{align*} \text{Shaded area} & = \text{Area of circle - Area of square} \\& = \pi r^2 - a^2 \\ & = 3.14\times 2^2 - (2\sqrt2)^2 \\ & = 12.56 - 8 \\ & = 4.56 \text{cm}^2\end{align*}

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