Project 8 : Area and Perimeter

Project 8 : Understanding Area and Perimeter

This project will help you understand how the perimeter and area of different shapes change when formed using the same length of wire. You will explore the properties of a circle, square, and rectangle and compare their areas while keeping the perimeter constant.

Objective:

To compare the perimeter and area of different 2D shapes made from the same length of wire (1 meter), and understand which shapes maximize area.

Materials Required:

• 1-meter long flexible wire or string ( You may use different length of the string)
• Ruler or measuring tape
• Compass and geometry tools
• Calculator (optional)
• Chart paper or math notebook for presentation
• Pencil, eraser, and colored pens

Instructions:

1. Take a 1-meter long wire and bend it into the shape of a **circle**.
   - Use the formula for circumference: C = 2πr to calculate the radius.
   - Measure and record the radius.
   - Calculate the area using A = πr².

2. Straighten the wire and now bend it into a **square**.
   - Each side = Total length ÷ 4 = 25 cm.
   - Calculate area using A = side².

3. Now form a **rectangle** with length = 30 cm and breadth = 20 cm.
   - Confirm that perimeter is still 100 cm.
   - Calculate area using A = length × breadth.

Record Your Observations:

Shape	Dimensions	Perimeter (cm)	Area (cm²)
Circle		100
Square		100
Rectangle		100

Reflection Questions:

1. Which shape had the maximum area?
2. Did all shapes have the same perimeter?
3. What do you observe about the relationship between perimeter and area?
4. In real-life scenarios (e.g., fencing), which shape would you prefer if you want to enclose the maximum space?
5. What conclusions can you draw from this activity?

Presentation Guidelines:

• Submit a neatly labeled chart or notebook page with diagrams of all three shapes.
• Show all calculations clearly.
• Use a comparison table and include your answers to the reflection questions.
• You may decorate your work neatly to make it visually appealing.

Students may use different measures and different presentation formats. Given above is a rough outline.

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