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

24 square units
24 square units

48 square units
48 square units

36 square units
36 square units

30 square units

1 answer

To find the area of the composite figure described in the problem, let's break it down step by step.

  1. Identify the shape of the figure: The figure can be visualized as a large rectangle (main part) from which a smaller rectangle (the missing piece) is removed from the center left side.

  2. Dimensions of the large rectangle:

    • The top side is 6 units.
    • The bottom side is 6 units (so the top and bottom sides are equal).
    • The right side is 8 units.

    This indicates that the dimensions of the large rectangle are 6 units (width) and 8 units (height).

  3. Calculate the area of the large rectangle: \[ \text{Area}_{\text{large rectangle}} = \text{width} \times \text{height} = 6 \times 8 = 48 \text{ square units} \]

  4. Identify the dimensions of the missing rectangle:

    • The vertical width of the missing rectangle on the left is 2 units from the top seen in the description.
    • The height of the missing rectangle is represented as the remaining height of the large rectangle after the missing part, which appears to be (8 - 2) = 6 units.

    Therefore, it seems that the missing rectangle has dimensions of 2 units (width) by 6 units (height).

  5. Calculate the area of the missing rectangle: \[ \text{Area}_{\text{missing rectangle}} = \text{width} \times \text{height} = 2 \times 6 = 12 \text{ square units} \]

  6. Calculate the area of the composite figure: To find the area of the figure, we will subtract the area of the missing rectangle from the area of the large rectangle: \[ \text{Area}{\text{figure}} = \text{Area}{\text{large rectangle}} - \text{Area}_{\text{missing rectangle}} = 48 - 12 = 36 \text{ square units} \]

Given this calculation, the area of the figure is 36 square units.

Final answer: 36 square units.