The figure shows a square inscribed in a circle of radius r = 7.53 cm.
The yellow region corresponds to the area of the circle minus the area of the square.
The area of a circle of radius r is:
[tex]A_c=\pi r^2[/tex]
Calculating:
[tex]A_c=\pi(7.53\text{ cm})^2=178.13\text{ }cm^2[/tex]
The radius of the circle is half the diagonal of the square. The diagonal of the square is:
d = 2 x 7.53 cm = 15.06 cm
The area of a square, given the diagonal d, is calculated as follows:
[tex]A_s=\frac{d^2}{2}[/tex]
Calculating:
[tex]\begin{gathered} A_s=\frac{(15.06\text{ cm})^2}{2} \\ \\ A_s=113.40\text{ }cm^2 \end{gathered}[/tex]
The required area is:
A = 178.13 - 113.40 = 64.73 square cm
