The figure is formed from rectangles. Find the total area. The diagram is not to scale.

Question

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

Answer 1

To find the total area of the given polygon, we can break it down into rectangles and subtract the area of the missing (cut out) corner.

First, let's consider the large rectangle, which would exist if the top right corner wasn't cut out:
- Width = 8 feet (given)
- Height = 5 feet (given)
The area of this large rectangle would be: \( 8 \text{ ft} \times 5 \text{ ft} = 40 \text{ ft}^2 \)

Now, let's consider the area of the cut-out rectangle at the top right:
- Width = 3 feet (given)
- Height = 5 - 3 = 2 feet (the difference between the total height and the labeled vertical side)
The area of the cut-out rectangle would be: \( 3 \text{ ft} \times 2 \text{ ft} = 6 \text{ ft}^2 \)

To find the area of the polygon, we subtract the area of the cut-out rectangle from the area of the larger rectangle:
Total area = Area of large rectangle - Area of cut-out rectangle
Total area = \( 40 \text{ ft}^2 - 6 \text{ ft}^2 = 34 \text{ ft}^2 \)

Therefore, the total area of the polygon is \( 34 \text{ ft}^2 \).