Math Problem Statement
Solution
The problem requires us to find the area of the shaded region, which is formed by removing a rectangle from a right triangle.
Step 1: Find the area of the right triangle.
The formula for the area of a triangle is:
- Base = 6 m
- Height = 4 m
Step 2: Find the area of the rectangle.
The area of a rectangle is given by:
- Length = 2 m
- Width = 3 m
Step 3: Calculate the area of the shaded region.
The shaded region is the area of the triangle minus the area of the rectangle:
Final Answer:
The area of the shaded region is .
Would you like further details or clarifications? Here are some related questions:
- What would happen if the rectangle dimensions changed?
- How do you calculate the area of other polygons?
- What is the significance of using the correct units in geometry problems?
- How do you find the perimeter of the shaded region in this problem?
- Can this problem be solved using coordinate geometry?
Tip: Always ensure that units are consistent throughout the calculation to avoid mistakes!
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Math Problem Analysis
Mathematical Concepts
Geometry
Area Calculation
Subtraction of Areas
Formulas
Area of Triangle = 1/2 * base * height
Area of Rectangle = length * width
Theorems
Basic Area Theorem
Subtraction Theorem for Composite Areas
Suitable Grade Level
Grades 5-7
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