Use the image to answer the question.
An illustration shows a polygon where the top, right, and bottom sides are perpendicular to each other. A smaller rectangular piece is missing from the center of the left side of the polygon inward. The dimensions are as follows: the top side is 6, the right side is 8, and the bottom side is 6. The left side is divided into three parts. It shows a vertical width of 2 from the top
Solve the following problem using what you know about composite figures. What is the area of the figure?
(1 point)
Responses
30 square units
30 square units
48 square units
48 square units
36 square units
36 square units
24 square units
24 square units
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The correct answer is 36 square units.
To find the area of the figure, we need to find the area of the polygon and then subtract the area of the missing rectangle.
The area of the polygon can be found by multiplying the lengths of the sides:
Area of the polygon = length × width = 6 × 8 = 48 square units.
The missing rectangle's dimensions are given as a vertical width of 2. To find the length, we subtract the length of the bottom and top sides from the total length of the left side:
Length of missing rectangle = (6 - 2 -2) = 2 square units.
Now we can find the area of the missing rectangle:
Area of missing rectangle = length × width = 2 × 2 = 4 square units.
Finally, we subtract the area of the missing rectangle from the area of the polygon:
Area of figure = Area of polygon - Area of missing rectangle = 48 - 4 = 36 square units.