The figure is formed from rectangles. Find the total area. The diagram is not to scale.
An abnormally shaped polygon with 6 sides is shown.
An abnormally shaped polygon with 6 sides is shown. The polygon has a shape similar to a rectangle, but with the top right corner cut out. Starting on the far left side of the shape, there is a vertical side labeled 5 feet. Moving counterclockwise around the shape, there is a horizontal side along the bottom labeled 8 feet. There is a vertical side on the right side of the image labeled 3 feet. There is a horizontal side that cuts back into the shape labeled 3 feet. There is a vertical side extending up with no label. The final side is horizontal and connects this vertical side with the first vertical side that was labeled 5 feet. This side, which is at the top of the shape, has no label.
(1 point)
Responses
40 ft2
40 ft 2
34 ft2
34 ft 2
73 ft2
73 ft 2
26 ft2
To find the total area of the given 6-sided polygon, we can break it down into simple rectangles or subtract the smaller rectangle from a larger one.
We start with a large rectangle, the dimensions of which can be found using the sides that are given. From the far left, we have a side that is 5 feet tall; from the bottom, there is a horizontal side that is 8 feet wide. We use these dimensions to determine the area of the larger rectangle:
Area of larger rectangle = height × width = 5 feet × 8 feet = 40 square feet.
Now, looking at the top right corner that is cut out, we can treat it as a smaller rectangle subtracted from the larger one. This smaller rectangle can be defined by the right side that is 3 feet tall and adjacent top side that is 3 feet wide:
Area of smaller rectangle = height × width = 3 feet × 3 feet = 9 square feet.
Lastly, to find the area of the original polygon, we subtract the area of the smaller rectangle from the larger one:
Total area of polygon = Area of larger rectangle - Area of smaller rectangle
Total area of polygon = 40 ft² - 9 ft² = 31 ft²
So the total area of the polygon is 31 square feet. However, this option isn't listed among the possible responses. Let's check the geometrical description given once more:
- The overall width of the original uncut rectangle is 8 feet.
- The missing top right rectangle has a width of 3 feet.
Make sure that the width of the missing rectangle subtracts directly from the overall width of the original rectangle. This would be true if the full width of the original rectangle carries through to the part above the missing rectangle. Since the diagram's scale or more specific layout isn't provided, if there's no error in the problem description, choosing an answer from the given options is impossible given our calculation, and there might be an error in the provided answers.
It's possible that there could be a misunderstanding or misinterpretation of the given problem without a visual. Since none of the provided responses match the calculated area of 31 ft², you may want to double-check the problem statement or diagram for any missing or additional information.