Find the area of the figure to the nearest tenth. [Pic]

Question
Solid Geometry
asked 2020-12-29
Find the area of the figure to the nearest tenth. [Pic]

Answers (1)

2020-12-30
I guess we're supposed to know that the shape on the right is a half-circle. So then this is basically just a square with a half-circle bite taken out of it.
So let's calculate the area of the square before Pacman came along and chewed on it.
Area of the square=\(\displaystyle{\left({6}{f}{t}\right)}×{\left({6}{f}{t}\right)}={36}{f}{t}^{{2}}\)
Now let's figure out how much area is missing. The area is half of a circle with diameter 6 ft. So its radius is 3 ft. The area of a whole circle is given by π×radius^2. So the area of the missing part is
Area of half of a circle=\(\displaystyle\frac{{1}}{{2}}×{3.14}×{\left({3}{f}{t}\right)}^{{2}}={14.1}{f}{t}^{{2}}\)
Now we know that the area of the green part is just the area of the full square minus the area of the part that's missing. Hence
Area=\(\displaystyle{36}{f}{t}^{{2}}−{14.1}{f}{t}^{{2}}\)
Area=\(\displaystyle{21.9}{f}{t}^{{2}}\)
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