Math Problem Statement

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

Solution

To find the area of the piecewise rectangular figure, we break it into smaller rectangles, calculate their individual areas, and sum them up.


Step-by-Step Breakdown

The figure can be divided into three rectangles as follows:

  1. Top Rectangle (largest rectangle at the top):

    • Width = 9 in
    • Height = 9 in
    • Area = 9×9=81in29 \times 9 = 81 \, \text{in}^2
  2. Left Bottom Rectangle:

    • Width = 2 in
    • Height = 4 in
    • Area = 2×4=8in22 \times 4 = 8 \, \text{in}^2
  3. Right Bottom Rectangle:

    • Width = 2 in
    • Height = 4 in
    • Area = 2×4=8in22 \times 4 = 8 \, \text{in}^2

Total Area:

Now, sum up the areas of all three rectangles:

Total Area=81+8+8=97in2\text{Total Area} = 81 + 8 + 8 = 97 \, \text{in}^2


Final Answer:

The total area of the figure is 97 square inches.


Do you need further clarification or a visual breakdown? Let me know!


Related Questions:

  1. How do you calculate the area of irregular figures?
  2. How can we generalize area formulas for more complex shapes?
  3. What is the perimeter of this figure?
  4. How would the area change if the height of one rectangle increased?
  5. How can you divide more complex figures into rectangles or triangles?

Tip: Always break complex shapes into familiar, smaller components (rectangles, triangles, etc.) to simplify area calculations.

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Math Problem Analysis

Mathematical Concepts

Geometry
Area of Rectangles
Piecewise Rectangular Figures

Formulas

Area = Width × Height

Theorems

Decomposition of irregular shapes into smaller rectangles

Suitable Grade Level

Grades 6-8