give an arithmetic series is (7/6) + (11/6) + (5/2) + (19/6) ... + (119/6). find the number of terms in the series

 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 as shorthand.