Instructions
Welcome, junior designer! You are helping to plan a new community garden. You need to calculate the space and materials needed for four different plots. Follow these steps carefully:
- Review the definitions of Perimeter and Area in Section 1.
- Calculate the Perimeter (P) and Area (A) for each proposed rectangular plot in the table in Section 2. Assume all measurements are in meters (m).
- Use your calculations from Section 2 to complete the budget questions in Section 3.
- Complete the Challenge Corner for extra credit!
Section 1: Reviewing Core Concepts
Perimeter and Area are two important measurements for building. Assume every unit used in the activity is 1 meter (1m).
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Perimeter (P): The total distance around the outside of a shape. It tells us how much fencing we need. Formula for Rectangle: P = Side A + Side B + Side A + Side B
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Area (A): The total space covered inside a shape. It tells us how much soil or paving stones we need. Formula for Rectangle: A = Side A $\ imes$ Side B
Example: A plot is 3 meters by 4 meters.
- P = 3 + 4 + 3 + 4 = 14 meters
- A = 3 $\ imes$ 4 = 12 square meters
Section 2: Calculating Garden Plots
Complete the table below. Remember to include the correct units (meters or square meters) in your answers.
| Plot Name | Side A (m) | Side B (m) | Perimeter (m) | Area (sq. m) |
|---|---|---|---|---|
| Example | 5 | 2 | 14 meters | 10 sq. meters |
| Plot 1 (Square) | 4 | 4 | ||
| Plot 2 (Standard) | 6 | 3 | ||
| Plot 3 (Narrow) | 10 | 1 | ||
| Plot 4 (Large) | 7 | 5 | ||
| Plot 5 (Custom) | 8 | 4 |
Section 3: Budgeting and Materials
The garden manager needs to know the cost of materials before construction begins. Use the following pricing:
- Fencing Cost: $5 per meter of perimeter.
- Soil Cost: $2 per square meter of area.
Task 1: Cost of Plot 2 (6m x 3m)
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What is the Perimeter of Plot 2? (From Section 2)
$P = $
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What is the cost of fencing Plot 2? (P $\ imes$ $5)
Fencing Cost = $
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What is the Area of Plot 2? (From Section 2)
$A = $
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What is the cost of soil for Plot 2? (A $\ imes$ $2)
Soil Cost = $
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What is the TOTAL cost to create Plot 2 (Fencing Cost + Soil Cost)?
Total Cost = $
Task 2: Comparison Shopping (Multiple Choice)
Which plot costs less overall: Plot 1 (4m x 4m) or Plot 3 (10m x 1m)?
(Show your work below, then circle the answer.)
- Cost for Plot 1: $
- Cost for Plot 3: $
Circle One: Plot 1 OR Plot 3
Section 4: Challenge Corner (Optional)
This section requires careful thinking about measurement relationships.
- Design Challenge: The community needs a plot that has an Area of exactly 24 square meters. Draw three different rectangles below that meet this area requirement (use side lengths that are whole numbers).
| Design | Side A (m) | Side B (m) | Area (sq. m) | Perimeter (m) |
|---|---|---|---|---|
| A | 6 | 4 | 24 | 20 |
| B | 24 | |||
| C | 24 | |||
| D | 24 |
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Reflection: If the garden budget is very tight, which of your four designs (A, B, C, or D) would be the best choice to build, and why? (Hint: Think about which design minimizes the cost of fencing.)
The best choice is Design _________ because:
Answer Key
Section 2: Calculating Garden Plots
| Plot Name | Side A (m) | Side B (m) | Perimeter (m) | Area (sq. m) |
|---|---|---|---|---|
| Example | 5 | 2 | 14 meters | 10 sq. meters |
| Plot 1 (Square) | 4 | 4 | 16 meters | 16 sq. meters |
| Plot 2 (Standard) | 6 | 3 | 18 meters | 18 sq. meters |
| Plot 3 (Narrow) | 10 | 1 | 22 meters | 10 sq. meters |
| Plot 4 (Large) | 7 | 5 | 24 meters | 35 sq. meters |
| Plot 5 (Custom) | 8 | 4 | 24 meters | 32 sq. meters |
Section 3: Budgeting and Materials
Task 1: Cost of Plot 2 (6m x 3m)
- Perimeter (P): 18 meters
- Fencing Cost: 18 $\ imes$ $5 = $90
- Area (A): 18 sq. meters
- Soil Cost: 18 $\ imes$ $2 = $36
- TOTAL cost: $90 + $36 = $126
Task 2: Comparison Shopping
- Plot 1 (4m x 4m): P=16, A=16. Fencing: $80. Soil: $32. Total Cost: $112
- Plot 3 (10m x 1m): P=22, A=10. Fencing: $110. Soil: $20. Total Cost: $130
Circle One: Plot 1 OR Plot 3
Section 4: Challenge Corner (Example Solutions)
- Design Challenge Solutions (Area = 24 sq. m):
| Design | Side A (m) | Side B (m) | Area (sq. m) | Perimeter (m) |
|---|---|---|---|---|
| A | 6 | 4 | 24 | 20 |
| B | 8 | 3 | 24 | 22 |
| C | 12 | 2 | 24 | 28 |
| D | 24 | 1 | 24 | 50 |
- Reflection: The best choice is Design A (6m x 4m) because it has the smallest Perimeter (20m) for that Area, which means it requires the least amount of expensive fencing. Plots that are closer to a square shape usually have a smaller perimeter than long, skinny plots for the same area.