Question

1. a square flooring tile has a circular design printed on it. if the tile is 20 cm long on each side, what is the area of the tile not covered by the design?

Explanation:

Step1: Calculate the area of the square

The area formula of a square is \(A_{square}=s^2\), where \(s = 20\) cm.
\(A_{square}=20\times20=400\) \(cm^{2}\)

Step2: Calculate the area of the circle

The diameter of the circle \(d = 20\) cm, so the radius \(r=\frac{d}{2}=10\) cm.
The area formula of a circle is \(A_{circle}=\pi r^{2}\), taking \(\pi = 3.14\).
\(A_{circle}=3.14\times10^{2}=3.14\times100 = 314\) \(cm^{2}\)

Step3: Calculate the area not covered by the design

Subtract the area of the circle from the area of the square.
\(A=A_{square}-A_{circle}\)
\(A = 400 - 314=86\) \(cm^{2}\)

Answer:

\(86\) \(cm^{2}\)