Math Problem Statement

Find the perimeter of the figure below: (Take π = 22/7)

Solution

To solve this problem, let’s break down how to find the perimeter of the given shape.

The shape consists of:

  1. A rectangular base with length 18 m and height 6 m.
  2. 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:

  1. 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: 6+6+18=306 + 6 + 18 = 30 m.
  2. Circumference of the Full Circle on Top:

    • Since the diameter of the circle is 6 m, its radius rr is 62=3\frac{6}{2} = 3 m.
    • Using π=227\pi = \frac{22}{7}, the circumference CC of the circle is: C=2πr=2×227×3=132718.86 mC = 2 \pi r = 2 \times \frac{22}{7} \times 3 = \frac{132}{7} \approx 18.86 \text{ m}
  3. Total Perimeter:

    • Add the perimeter of the rectangle (30 m) and the circumference of the circle (18.86 m): Total Perimeter=30+18.86=48.86 m\text{Total Perimeter} = 30 + 18.86 = 48.86 \text{ 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:

  1. How do you calculate the circumference of a circle if only the diameter is given?
  2. Why is only half the circumference of a full circle used if it were a semicircle?
  3. How does changing the value of π\pi affect the answer?
  4. What would happen to the perimeter if the rectangle’s width was increased?
  5. 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