Find the area of the figure.(Sides meet at right angles.)3in1in2in4in2in1in3in2insquareinches

1. Break Down the Problem

To find the area of the figure, we can split it into smaller rectangles whose dimensions are provided.

2. Relevant Concepts

The area $A$ of a rectangle can be calculated using the formula: $A = \text{length} \times \text{width}$

3. Analysis and Detail

Let's identify the sections of the figure:

• Rectangle 1: 3 in (length) × 1 in (width)
• Rectangle 2: 2 in (length) × 4 in (width)
• Rectangle 3: 2 in (length) × 1 in (width)
• Rectangle 4: 3 in (length) × 2 in (width)
• Rectangle 5: 2 in (length) × 1 in (width)

Now we will calculate the area for each rectangle:

1. Area of Rectangle 1: $A_1 = 3 \times 1 = 3 \text{ square inches}$

2. Area of Rectangle 2: $A_2 = 2 \times 4 = 8 \text{ square inches}$

3. Area of Rectangle 3: $A_3 = 2 \times 1 = 2 \text{ square inches}$

4. Area of Rectangle 4: $A_4 = 3 \times 2 = 6 \text{ square inches}$

5. Area of Rectangle 5: $A_5 = 2 \times 1 = 2 \text{ square inches}$

4. Verify and Summarize

Now, we will sum up the areas: $\text{Total Area} = A_1 + A_2 + A_3 + A_4 + A_5$ $\text{Total Area} = 3 + 8 + 2 + 6 + 2 = 21 \text{ square inches}$

Final Answer

The total area of the figure is $\boxed{21}$ square inches.