Answer:
Step-by-step explanation:
We have to assume that the square tarp, although it obviously won't cover the circular emblem, does touch the edge of the circle in 4 places (those 4 places would be the midpoint of each side of the square. That's the only way this would work!) With that being said, and also knowing that the square covers 196 square feet, we can find the length of one of the sides of the square by using the area formula for a square:
[tex]A=s^2[/tex] We know the area is 196, so
[tex]196=s^2[/tex] which means that the square's sides measure 14 feet each. Going through the middle of the square which is also the middle of the circle means that the diameter of the circle is 14. Which also means that its radius is 7 feet. The area formula for a circle is:
[tex]A=\pi r^2[/tex]
If the radius is 7, and 7 squared is 49, then the area of the circle in terms of pi is
A = 49π feet squared
The area of the circular emblem is 49π square feet if the tarp covers an area of 196 square feet.
It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)
We have:
A freshly-painted circular emblem on a football field is completely covered by the smallest possible square tarp.
196 = s²
s = 14 feet
Diameter of the circle = 14 feet
The radius of the circle = 7 feet
The area of the circular emblem = π(7²) = 49π square feet
Thus, the area of the circular emblem is 49π square feet if the tarp covers an area of 196 square feet.
Learn more about circle here:
brainly.com/question/11833983
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