Math Problem Statement
Solution
The figure shown in the image is a compound shape made up of rectangles. To find the total area, we need to break the figure into simpler rectangular sections and sum their areas.
Step-by-step breakdown:
-
First Rectangle (Left side):
- Dimensions: 5 m by 10 m.
- Area = .
-
Second Rectangle (Top right):
- Dimensions: 14 m by 6 m.
- Area = .
-
Third Rectangle (Bottom right):
- Dimensions: 6 m by 2 m.
- Area = .
-
Fourth Rectangle (Right bottom corner):
- Dimensions: 3 m by 2 m.
- Area = .
Now, sum up the areas:
Thus, the area of the figure is 152 square meters.
Would you like further clarification or more details? Here are a few related questions to consider:
- How can you find the perimeter of this compound figure?
- What would happen to the total area if one of the rectangles changed in size?
- How can you break down a compound shape into different shapes, like triangles?
- How do you calculate the area of a triangle, and when would you use it?
- How can you verify the correctness of your solution by reconstructing the figure?
Tip: Always label each part of a compound figure clearly, so it’s easier to break down into smaller shapes for calculating areas.
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Math Problem Analysis
Mathematical Concepts
Geometry
Area of Compound Figures
Rectangles
Formulas
Area of a rectangle = length × width
Theorems
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Suitable Grade Level
Grades 6-8
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