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
1 answer