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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

36 square units
36 square units

30 square units

24 square units

48 square units

1 answer

To find the area of the given composite figure, we can break it down into two main parts: the larger rectangle and the missing rectangular piece.

  1. Determine the area of the larger rectangle:

    • The width (top or bottom) is 6 units.
    • The height (right side) is 8 units.
    • Area of the larger rectangle = width × height = 6 × 8 = 48 square units.

  2. Determine the area of the missing rectangular piece:

    • The vertical height of the missing piece is 2 units (from the top as given).
    • The width (conforming to the left side) can be determined since the left side of the figure is divided into 3 parts, and the total height of the figure is 8 units. The remaining part of the left side under the missing piece is (8 - 2) = 6 units.
    • The width of the missing rectangular piece can be found since no explicit width is provided in your description, but based on the setup of the figure, we can assume that the missing piece takes up the left vertical portion of the width of 2 units.
    • Area of the missing rectangular piece = width × height = 2 × 2 = 4 square units.

  3. Calculate the area of the figure:

    • Total area of the figure = Area of the larger rectangle - Area of the missing rectangle = 48 square units - 4 square units = 44 square units.

While the above calculation shows the area calculation method, none of the provided response options (36, 30, 24, 48 square units) match the calculated total of 44 square units.

It’s recommended to double-check the dimensions or description for any possible misinterpretation or omission that might lead to a specific response option fitting.