Math Problem Statement
Solution
To solve this problem, let’s break down how to find the perimeter of the given shape.
The shape consists of:
- A rectangular base with length 18 m and height 6 m.
- Two semicircles on top, combined to form a full circle of diameter 6 m (equal to the width of the rectangle).
Steps to Find the Perimeter:
-
Perimeter of the Rectangle (excluding the top side):
- The rectangle has two vertical sides of 6 m each and a bottom side of 18 m.
- Total length of these three sides: m.
-
Circumference of the Full Circle on Top:
- Since the diameter of the circle is 6 m, its radius is m.
- Using , the circumference of the circle is:
-
Total Perimeter:
- Add the perimeter of the rectangle (30 m) and the circumference of the circle (18.86 m):
Final Answer:
The perimeter of the figure is approximately 48.86 meters.
Would you like more details on any of the steps?
Here are five questions to deepen understanding:
- How do you calculate the circumference of a circle if only the diameter is given?
- Why is only half the circumference of a full circle used if it were a semicircle?
- How does changing the value of affect the answer?
- What would happen to the perimeter if the rectangle’s width was increased?
- How can we apply similar steps to irregular shapes?
Tip: Always check if parts of a shape can form common shapes (like a full circle) to simplify perimeter or area calculations.
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Math Problem Analysis
Mathematical Concepts
Geometry
Perimeter
Circles and Semicircles
Rectangles
Formulas
Perimeter of a rectangle = 2 * (length + width)
Circumference of a circle = π * diameter
Theorems
Circumference theorem
Suitable Grade Level
Grades 6-8
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