# The square surface cover shown in the figure is 10.16 centimeters on each side. The knockout in the center of the cover has a diameter of 1.27 centimeters. Find the area of the cover to the nearest hundredth centimeter.

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The square surface cover shown in the figure is 10.16 centimeters on each side. The knockout in the center of the cover has a diameter of 1.27 centimeters. Find the area of the cover to the nearest hundredth centimeter.

2020-11-09
The area of the cover is the area of the square minus the area of the circle: Acover=Asquare-Acircle Acover=$$\displaystyle{8}^{{2}}-\frac{{π{d}^{{2}}}}{{4}}$$
Substitute s=10.16 cm and d=1.27 cm: Acover=$$\displaystyle{10.16}^{{2}}-{\left(π\frac{{\left({1.27}\right)}^{{2}}}{{4}}\right.}$$
Use a calculator and round to the nearest hundredth cm (2 decimal places):
Acover≈101.96 cm

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