Question
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
48 square units
48 square units
30 square units
30 square units
36 square units
36 square units
24 square units
24 square units
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Answers
GPT-4o mini
To find the area of the composite figure described, we can break it down into its components based on the information given:
1. The overall shape is a polygon with a top side of 6 units, a bottom side of 6 units, and a right side of 8 units.
2. The left side has a segment of 2 units from the top, indicating the height of a missing rectangular piece.
### Step 1: Calculate the area of the larger rectangle.
The base of the rectangle is 6 units and the height is 8 units:
\[
\text{Area of the larger rectangle} = \text{base} \times \text{height} = 6 \times 8 = 48 \text{ square units}
\]
### Step 2: Calculate the area of the missing rectangular piece.
The missing rectangular piece has a height of 2 units extending down the left side. We need the width of this piece to calculate its area. The width of the missing section was not given but based on the description, it is likely that it stretches across the left side (the missing rectangle is assumed to have a width equal to the base of the figure, which is 6 units here).
\[
\text{Area of the missing rectangle} = \text{width} \times \text{height} = 2 \times 6 = 12 \text{ square units}
\]
### Step 3: Calculate the area of the figure by subtracting the area of the missing rectangle from the area of the larger rectangle.
\[
\text{Area of the figure} = \text{Area of the larger rectangle} - \text{Area of the missing rectangle} = 48 - 12 = 36 \text{ square units}
\]
### Conclusion
The area of the composite figure is **36 square units**.
**Final Response: 36 square units**
1. The overall shape is a polygon with a top side of 6 units, a bottom side of 6 units, and a right side of 8 units.
2. The left side has a segment of 2 units from the top, indicating the height of a missing rectangular piece.
### Step 1: Calculate the area of the larger rectangle.
The base of the rectangle is 6 units and the height is 8 units:
\[
\text{Area of the larger rectangle} = \text{base} \times \text{height} = 6 \times 8 = 48 \text{ square units}
\]
### Step 2: Calculate the area of the missing rectangular piece.
The missing rectangular piece has a height of 2 units extending down the left side. We need the width of this piece to calculate its area. The width of the missing section was not given but based on the description, it is likely that it stretches across the left side (the missing rectangle is assumed to have a width equal to the base of the figure, which is 6 units here).
\[
\text{Area of the missing rectangle} = \text{width} \times \text{height} = 2 \times 6 = 12 \text{ square units}
\]
### Step 3: Calculate the area of the figure by subtracting the area of the missing rectangle from the area of the larger rectangle.
\[
\text{Area of the figure} = \text{Area of the larger rectangle} - \text{Area of the missing rectangle} = 48 - 12 = 36 \text{ square units}
\]
### Conclusion
The area of the composite figure is **36 square units**.
**Final Response: 36 square units**