https://file.aiquickdraw.com/mathbot/file/1726673812803gsflz5vj.jpg

To find the area of this irregular figure, we can break it down into smaller, manageable shapes (rectangles and triangles). Let's proceed step by step:

### Step 1: Break down the figure
The figure consists of:
1. **A rectangle** on the far right.
2. **A trapezoid** in the middle.
3. **Another rectangle** at the bottom left.
4. **A triangle** on the top left.

### Step 2: Calculate the area of each shape

#### 1. Right Rectangle:
- **Dimensions**: 4 inches (width) × 8 inches (height)
- **Area**: \(4 \times 8 = 32 \, \text{square inches}\)

#### 2. Middle Trapezoid:
- The height is 5 inches (given).
- The two parallel sides are 1 inch (top) and 5 inches (bottom).
- **Area of trapezoid formula**: 
  \[
  \text{Area} = \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height}
  \]
  Substituting the values:
  \[
  \text{Area} = \frac{1}{2} \times (1 + 5) \times 5 = \frac{1}{2} \times 6 \times 5 = 15 \, \text{square inches}
  \]

#### 3. Bottom Left Rectangle:
- **Dimensions**: 5 inches (width) × 2 inches (height)
- **Area**: \(5 \times 2 = 10 \, \text{square inches}\)

#### 4. Top Left Triangle:
- **Base**: 3 inches
- **Height**: 2 inches
- **Area of triangle formula**: 
  \[
  \text{Area} = \frac{1}{2} \times \text{Base} \times \text{Height}
  \]
  Substituting the values:
  \[
  \text{Area} = \frac{1}{2} \times 3 \times 2 = 3 \, \text{square inches}
  \]

### Step 3: Total Area
Now, add up the areas of all the parts:
\[
\text{Total Area} = 32 + 15 + 10 + 3 = 60 \, \text{square inches}
\]

### Final Answer:
The area of the figure is **60 square inches**.

Would you like more details or clarifications? Here are some related questions to further your understanding:

1. How do you find the area of a trapezoid in general?
2. Can the area of an irregular shape always be broken into simpler parts?
3. What are the differences in calculating the area of polygons versus circles?
4. How would you calculate the area of a 3D object like a prism?
5. How does the concept of area extend to integration in calculus?

**Tip**: Always verify the breakdown of complex shapes by rechecking the dimensions and shape types before calculating the area.

What is the area of this figure? (The figure is a complex shape made up of two rectangles, one trapezoid, and one triangle, with given dimensions.)

Learn how to calculate the area of an irregular figure by breaking it down into simpler shapes like rectangles, trapezoids, and triangles. This problem involves key geometry concepts and is suitable for students in Grades 6-8. The total area is 60 square inches.

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