Math Problem Statement
Solution
The image you uploaded shows an irregular L-shaped figure with the following dimensions:
- Top horizontal length: 22 meters
- Bottom horizontal length: 13 meters
- Left vertical length: 17 meters
- Right vertical length: 23 meters
To calculate the area of this L-shaped figure, you can divide it into two rectangles. Let's break it down step by step:
Step 1: Divide the L-shape into two rectangles
-
Rectangle 1 (Upper part):
- Length = 22 meters
- Width = 13 meters
-
Rectangle 2 (Lower part):
- Length = (23 meters - 13 meters) = 10 meters
- Width = 17 meters
Step 2: Calculate the area of each rectangle
-
Area of Rectangle 1:
-
Area of Rectangle 2:
Step 3: Add the areas together
The total area of the L-shaped figure is the sum of the two rectangular areas:
So, the area of the L-shaped figure is 456 square meters.
Would you like more details or have any questions?
Related Questions:
- How would you find the perimeter of this L-shaped figure?
- Can the area be calculated using another method?
- How would you calculate the area if the L-shape had curves instead of straight lines?
- How does breaking complex shapes into simpler ones help in finding areas?
- What would be the effect on the area if one of the dimensions was doubled?
Tip:
When calculating the area of irregular shapes, breaking them down into simpler shapes (like rectangles, triangles, etc.) makes the process easier and more manageable.
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Math Problem Analysis
Mathematical Concepts
Geometry
Area Calculation
Decomposition of Shapes
Formulas
Area of a Rectangle = length × width
Theorems
Decomposition Method for Area Calculation
Suitable Grade Level
Grades 6-8