Math Problem Statement
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Solution
Based on the provided indicators in the image, I'll create a math problem that involves drawing geometric shapes to clarify and facilitate problem-solving.
Problem:
In a park, there is a triangular flower bed surrounded by a circular pathway. The radius of the circular pathway is 10 meters, and the flower bed forms an equilateral triangle with each side measuring 12 meters. Draw the geometric layout of this park area to help visualize the problem.
Questions:
- What is the area of the circular pathway?
- What is the area of the triangular flower bed?
- How much space is left between the circular pathway and the triangular flower bed?
- If the flower bed is expanded to reach the edge of the circular pathway, what would be the new side length of the triangle?
- How would the perimeter of the pathway change if the radius is increased by 2 meters?
Tip: Visualizing geometric relationships can simplify complex area and perimeter calculations.
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Math Problem Analysis
Mathematical Concepts
Geometry
Geometric Shapes
Area and Perimeter
Formulas
Area of a circle: A = πr²
Area of an equilateral triangle: A = (√3/4) × side²
Perimeter of a circle: P = 2πr
Theorems
Properties of equilateral triangles
Properties of circles
Suitable Grade Level
Grades 7-9
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