Part A
To find the area of the unshaded region, subtract the area of the shaded region from the sum of the areas of the rectangle and semicircle
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Explanation:
When it comes to area problems, think of a grid of squares. Let's say we had a 10 by 10 grid of tiny squares (10*10 = 100 total). Now let's say 8 of them are shaded in. There are 100 - 8 = 92 unshaded squares to represent the total area of the unshaded region.
That's effectively what's going on with this problem as well. Sure things get a bit tricky with that curved portion on top, but we can still get an approximation if we use smaller and smaller grid sizes. I recommend using graph paper or graphing software that provides a grid.
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Part B
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Explanation:
For now, I'm going to ignore the shaded region. I'll come back to it later.
The rectangle is 15 ft by 50 ft. It has an area of length*width = 15*50 = 750 sq ft.
The semicircle up top has an area of [tex]0.5*\pi r^2 = 0.5*\pi*(7.5)^2 \approx 88.3573[/tex] sq ft approximately. The 7.5 is from dividing the diameter in half to get the radius. As the instructions stated, I used the calculator's version of pi.
The rectangle and semicircle have their areas add to
750+88.3573 = 838.3573
Now we can finally address the shaded region. It is a 3 ft by 9 ft rectangle because "the length is 3 times the width" and the width is 3 ft. This shaded rectangle has area 3*9 = 27 sq ft.
The unshaded region is:
unshaded = total - shaded = 838.3573 - 27 = 811.3573
This rounds to the final answer of 811