Math Problem Statement
What is the area of the rectangle?
Solution
To calculate the area of the shape shown, it appears to be a composite figure rather than a simple rectangle. The figure can be split into basic geometric shapes like rectangles and triangles for easier calculation.
Let's break it down:
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Step 1: The main section is a rectangle with a width of 14 meters and a height of 18 meters.
- Area of this rectangle = .
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Step 2: There is a triangular portion that cuts into the upper-left side of the shape.
- The base of this triangle is the remaining portion after subtracting 14 meters from the total width of 20 meters. So, base of the triangle = .
- The height of the triangle is given as 11 meters.
- Area of this triangle = .
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Step 3: The total area of the composite shape is the area of the rectangle minus the area of the triangular cut-out.
Final Answer:
The total area of the shape is 219 square meters (m²).
Would you like a detailed breakdown of the steps, or do you have any other questions? Here are a few related questions to explore:
- How do you calculate the perimeter of this composite shape?
- What would happen if the triangle was not subtracted but added to the shape?
- How can you confirm the dimensions of complex shapes in real-life measurements?
- Can you apply the same method to calculate the area of a trapezoidal section?
- How does the area formula for a triangle differ from other polygon shapes?
Tip: Always try to break down complex shapes into simpler geometric figures for easier area calculations.
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Math Problem Analysis
Mathematical Concepts
Geometry
Composite Shapes
Area Calculation
Formulas
Area of a rectangle = length × width
Area of a triangle = ½ × base × height
Theorems
Basic Geometry Area Formulas
Suitable Grade Level
Grades 6-8
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