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

30 square units
30 square units

48 square units
48 square units

36 square units

Answer 1

To find the area of the polygon with a rectangular piece missing, we can break it down into manageable parts.

The larger polygon resembles a rectangle shape without the missing piece. Here are the dimensions given:

- The top side is 6 units.
- The bottom side is 6 units.
- The right side is 8 units.
- The left side is divided with a vertical section of 2 units from the top.

### Step 1: Calculate the area of the larger rectangle
The larger rectangle (including the missing piece) has a width of 6 units and a height of 8 units.

\[
\text{Area of the larger rectangle} = \text{width} \times \text{height} = 6 \times 8 = 48 \text{ square units}
\]

### Step 2: Calculate the area of the missing rectangular section
The missing rectangular piece has a vertical side length of 2 units (top part) and spans the entire height of the larger rectangle (which is 8 units). The horizontal length of the missing piece along the left side can be inferred as it stretches from the top down to the bottom at a certain height. Since the left vertical side has no specified width for the missing piece, we assume it encompasses the 2 units of height from the top to downward, making the missing section to be almost rectangular vertically cut out.

To calculate the area of the missing piece:
- The height is 2 units.
- The width is equivalent to the width of the larger polygon (which is 6 units).

\[
\text{Area of the missing rectangle} = \text{width} \times \text{height} = 2 \times 6 = 12 \text{ square units}
\]

### Step 3: Calculate the area of the remaining figure
To find the area of the remaining figure after the missing section is removed:

\[
\text{Area of the remaining figure} = \text{Area of the larger rectangle} - \text{Area of the missing rectangle}
\]
\[
\text{Area of the remaining figure} = 48 - 12 = 36 \text{ square units}
\]

Therefore, the area of the figure is **36 square units**.

### Final Response
**36 square units**