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

36 square units
36 square units

48 square units
48 square units

24 square units

1 answer

To determine the area of the composite figure described, we can break it down into rectangular sections.

  1. Dimensions of the outer rectangle:

    • Width (top and bottom): 6 units
    • Height (right side): 8 units
    • The area of the outer rectangle can be calculated as: \[ \text{Area}_{\text{outer}} = \text{width} \times \text{height} = 6 \times 8 = 48 \text{ square units} \]
  2. Dimensions of the missing rectangular piece:

    • The missing piece, located inward from the left side, has a vertical width of 2 units from the top. Based on the description, the height of the missing rectangular piece is not specified, but we can assume the height matches the vertical height of the outer rectangle minus the 2 units from the top.
    • Therefore, the height of the missing piece is \(8 - 2 = 6\) units.
    • The width of the missing piece can also be inferred as the depth that it goes inward from the left side. If it's a small center piece, we can assume it would be narrow (let's say 2 units across for the sake of computation).
    • The area of the missing piece can be calculated as: \[ \text{Area}{\text{missing}} = \text{width}{\text{missing}} \times \text{height}_{\text{missing}} = 2 \times 6 = 12 \text{ square units} \]
  3. Final computation of the area of the composite figure:

    • The area of the remaining figure is: \[ \text{Area}{\text{remaining}} = \text{Area}{\text{outer}} - \text{Area}_{\text{missing}} = 48 - 12 = 36 \text{ square units} \]

Thus, the area of the figure is \( \textbf{36 square units} \).