Answer: 65.01 square feet (approximate)
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Explanation:
The area of the rectangle is base*height = 7.5*5.5 = 41.25 square feet.
The quarter circle has the radius of 5.5 ft.
Consider a full circle with this same radius. The full circle would have area of
A = pi*r^2 = pi*(5.5)^2 = 30.25pi = 95.0331777710912
This value is approximate. The units are in square feet.
We don't want the full circle's area, but instead just a quarter of that. So we'll multiply by 1/4 = 0.25 to get
0.25*95.0331777710912 = 23.7582944427728
The area of the quarter circle is roughly 23.7582944427728 square feet.
The last step is to add the rectangle and quarter circle areas to get
41.25+23.7582944427728 = 65.0082944427728
This rounds to 65.01 when rounding to the nearest hundredth.
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If we wanted to do this in all one step, we could say
5.5*7.5 + 0.25*pi*(5.5)^2 = 65.0082944427729
which rounds to 65.01
The units of the answer are in square feet, in which we could write ft^2 or [tex]\text{ft}^2[/tex] as shorthand.
