Finding Unknown Perimeter Lengths

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📐 Part 1: Finding Unknown Sides of Squares

1. A square has a perimeter of 24 cm. What is the length of each side?

Formula: P = 4s, so s = P ÷ 4

Side length = _______ cm

2. The perimeter of a square garden is 36 metres. Find the length of one side.

Side length = _______ metres

3. Multiple Choice: If a square has a perimeter of 20 cm, what is the length of each side?

4 cm

5 cm

10 cm

80 cm

🔧 Part 2: Composite Shapes and Unknown Sides

4. The composite shape below has a total perimeter of 26 cm. The known sides are 5 cm, 4 cm, 3 cm, 6 cm, and 2 cm. Find the unknown side length.

Known sides: 5 + 4 + 3 + 6 + 2 = _______ cm

Unknown side = Total perimeter - Sum of known sides

Unknown side = _______ cm

5. A rectangular shape has an extra square attached. The rectangle is 8 cm by 6 cm, and the square has sides of 4 cm. If one side of the rectangle is shared with the square, what is the total perimeter?

Total perimeter = _______ cm

6. Write an algebraic expression: A composite shape has sides of 7 cm, x cm, 5 cm, and 9 cm. The total perimeter is 28 cm. Write an equation to find x.

Equation: _________________________

x = _______ cm

🏡 Part 3: Real-World Applications

7. Fencing Problem: Sarah wants to fence her rectangular vegetable garden. The garden is 12 metres long and 8 metres wide. However, one of the 8-metre sides is against her house and doesn't need fencing. How much fencing does Sarah need?

Fencing needed = _______ metres

8. Picture Frame: Tom is making a square picture frame. He has 140 cm of framing material. What is the maximum side length for his square frame?

Maximum side length = _______ cm

9. Challenge: A school playground has an L-shaped boundary. The measurements are: 20m, 15m, 8m, 10m, and 12m. One side length is unknown, but the total perimeter is 75m. Find the unknown side length and explain your method.

Unknown side = _______ metres

10. Reflection: Explain in your own words how you can use the perimeter formula to find unknown side lengths.