Math Problem Statement
Solution
The image shows a problem asking to find the area of shaded regions within a rectangle. Here's how we can solve it:
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Dimensions of the Rectangle:
The rectangle has a base and height .The area of the rectangle is given by:
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Unshaded Triangle:
The unshaded triangle is inside the rectangle with the same base and height. The base of the triangle is , and its height is also (since , the same as the rectangle's height).The area of a triangle is given by:
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Shaded Area:
The shaded region is the area of the rectangle minus the area of the triangle:
Thus, the shaded region has an area of 600 square feet.
Would you like more details or have any questions?
Here are five follow-up questions to expand understanding:
- How do we calculate the area of any general triangle?
- Why do we subtract the unshaded triangle's area from the rectangle's area to find the shaded regions?
- Can this method be applied to different shapes besides triangles, such as circles or trapezoids?
- How would the calculation change if the unshaded region were not triangular?
- What other methods could you use to check the area of the shaded region?
Tip: When calculating areas, make sure all dimensions are in the same units before performing any operations.
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Math Problem Analysis
Mathematical Concepts
Geometry
Area Calculation
Formulas
Area of Rectangle = base × height
Area of Triangle = 1/2 × base × height
Theorems
Basic Area Calculation
Suitable Grade Level
Grades 6-8
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