Math Problem Statement
Solution
To solve for the area of the shaded region, let's break the problem down step by step:
Step 1: Calculate the area of the larger rectangle
The larger rectangle has dimensions of 7 cm (length) by 5 cm (height).
Step 2: Calculate the area of the triangle (shaded region)
The shaded region is a triangle with a base of 4 cm and a height of 3 cm.
Step 3: The final area of the shaded region
The area of the shaded region (triangle) is simply the result we calculated in Step 2:
The area of the shaded region is .
Would you like further clarification on any part of this, or additional details? Here are some related questions to expand your understanding:
- How is the formula for the area of a triangle derived?
- What other methods can be used to calculate the area of irregular shapes?
- How can you verify if a triangle is a right triangle using its dimensions?
- How does the Pythagorean theorem relate to triangles and areas?
- What is the difference between finding the perimeter and area of geometric shapes?
Tip: When working with composite shapes, break them down into basic shapes like rectangles and triangles for easier calculations.
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Math Problem Analysis
Mathematical Concepts
Geometry
Area Calculation
Composite Shapes
Triangles
Rectangles
Formulas
Area of a rectangle = length × width
Area of a triangle = 1/2 × base × height
Theorems
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Suitable Grade Level
Grades 5-7
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