Area of Composite Figures Quick Check
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Question
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
24 square units
24 square units
36 square units
36 square units
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To find the area of the figure, we need to find the area of each individual shape and then add them together.
The top rectangle has a length of 6 and a width of 2, so its area is 6 x 2 = 12 square units.
The right rectangle has a length of 8 and a width of 6, so its area is 8 x 6 = 48 square units.
The bottom rectangle has a length of 6 and a width of 2, so its area is 6 x 2 = 12 square units.
To find the area of the missing rectangle, we need to find its length and width. We know that the total length of the left side is 6, and the vertical width of the missing rectangle is 2. So, the length of the missing rectangle is 6 - 2 = 4 units.
The missing rectangle has a length of 4 and a width of 2, so its area is 4 x 2 = 8 square units.
Now, we add up the areas of all the shapes: 12 + 48 + 12 + 8 = 80.
Therefore, the area of the figure is 80 square units.