https://file.aiquickdraw.com/mathbot/file/1727353408058j3rmjrgq.jpg

The figure provided resembles an L-shaped polygon. To calculate the area, we can divide the shape into two rectangles and sum their areas.

### Dimensions of the two rectangles:
1. **Top horizontal rectangle**:
   - Length: \(120\) units
   - Width: \(30\) units

2. **Bottom vertical rectangle**:
   - Height: \(80\) units
   - Width: \(55\) units

However, the height of the vertical rectangle includes the top part of the L-shape, which extends 30 units down. So, the actual height for the lower part of the L is \(80 - 30 = 50\) units.

### Calculation of area:
1. **Area of the top rectangle**:
   \[
   \text{Area}_1 = 120 \times 30 = 3600 \, \text{square units}
   \]

2. **Area of the bottom rectangle**:
   \[
   \text{Area}_2 = 55 \times 50 = 2750 \, \text{square units}
   \]

### Total area:
\[
\text{Total Area} = 3600 + 2750 = 6350 \, \text{square units}
\]

The area of the figure is **6350 square units**.

Would you like a detailed explanation of how to approach other similar problems, or have any questions about this one?

Here are 5 questions that build on this:
1. How would you calculate the perimeter of the same figure?
2. Can this shape be divided in any other way to find the area?
3. How would you calculate the area of a more complex polygonal figure?
4. What is the relation between perimeter and area for regular vs irregular shapes?
5. How would the calculation change if the figure were on a coordinate plane?

**Tip:** Breaking complex figures into simpler parts is a common strategy in geometry for easier calculation.

Learn how to find the area of an L-shaped figure by breaking it into two rectangles and summing their areas. This problem involves key geometric concepts and calculations. Suitable for students in Grades 6-8.

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