Math Problem Statement
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:
-
Top Rectangle (largest rectangle at the top):
- Width = 9 in
- Height = 9 in
- Area =
-
Left Bottom Rectangle:
- Width = 2 in
- Height = 4 in
- Area =
-
Right Bottom Rectangle:
- Width = 2 in
- Height = 4 in
- Area =
Total Area:
Now, sum up the areas of all three rectangles:
Final Answer:
The total area of the figure is 97 square inches.
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Related Questions:
- How do you calculate the area of irregular figures?
- How can we generalize area formulas for more complex shapes?
- What is the perimeter of this figure?
- How would the area change if the height of one rectangle increased?
- 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