Question

Find the area of the yellow region. Round to the nearest tenth. 7.53cm

Answer 1

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:

`A_c=\pi r^2`

Calculating:

`A_c=\pi(7.53\text{ cm})^2=178.13\text{ }cm^2`

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:

`A_s=(d^2)/(2)`

Calculating:

`\begin{gathered} A_s=\frac{(15.06\text{ cm})^2}{2} \\ \\ A_s=113.40\text{ }cm^2 \end{gathered}`

The required area is:

A = 178.13 - 113.40 = 64.73 square cm