Year 5 Area and Perimeter Worksheet for Math

Instructions

1. Read the definitions and formulas for Area and Perimeter provided at the start of each section.
2. Complete the calculations for basic shapes in Section 1.
3. Use the Landscape Design Table in Section 2 to plan garden dimensions.
4. Solve the composite shape problem in Section 3 by breaking it into smaller rectangles.
5. Try the Extension Challenge if you finish early!

Section 1: The Basics of Backyard Design

Before we build a park, we need to understand our measurements.

• Perimeter is the distance around the outside of a shape. (Formula for rectangle: $P = L + L + W + W$)
• Area is the total space inside a shape. (Formula for rectangle: $A = L \times W$)

Calculate the Perimeter and Area for the following rectangular zones:

1. The Sandbox: Length = 5m, Width = 3m

   • Perimeter: __ m
   • Area: __ m²

2. The Picnic Deck: Length = 8m, Width = 6m

   • Perimeter: __ m
   • Area: __ m²

3. The Dog Run: Length = 12m, Width = 4m

   • Perimeter: __ m
   • Area: __ m²

Section 2: The Landscape Design Table

You are designing different flower beds for a community garden. Fill in the missing measurements below.

Section 3: Composite Shapes (The L-Shaped Patio)

Sometimes, shapes aren't perfect rectangles. To find the area of an L-shape, split it into two smaller rectangles, find the area of each, and add them together.

Imagine an L-shaped patio with these dimensions:

• The vertical part of the L is 10m tall and 4m wide.
• The horizontal part attached to the bottom is 6m long and 3m tall.

Task:

1. What is the area of the first rectangle (10m x 4m)? ____ m²
2. What is the area of the second rectangle (6m x 3m)? ____ m²
3. What is the Total Area of the patio? ____ m²

Section 4: Real-World Logic

4. You have 20 meters of fencing. You want to create a rectangular vegetable patch with the largest possible area.
   • List two different sets of dimensions (Length and Width) that use exactly 20m of fencing:
     • Option A: Length m, Width m (Area = ____ m²)
     • Option B: Length m, Width m (Area = ____ m²)
   • Which option provides more space for growing vegetables? ____

Section 5: Extension Challenge

The Mystery Pool: The local pool has an Area of 48m². If the length of the pool is 8m, what is the Perimeter of the pool?

Hint: Find the width first!

Answer: ____ m

Answer Key

Section 1:

1. Perimeter: 16m | Area: 15m²
2. Perimeter: 28m | Area: 48m²
3. Perimeter: 32m | Area: 48m²

Section 2:

1. Tulips: P=20m, A=24m²
2. Sunflowers: P=22m, A=18m²
3. Lavender: P=28m, A=49m²
4. Carrots: P=28m, A=33m²
5. Herbs: P=20m, A=25m²

Section 3:

1. 40m²
2. 18m²
3. 58m²

Section 4:

• Possible pairs (L+W must equal 10): 9x1 (Area 9), 8x2 (Area 16), 7x3 (Area 21), 6x4 (Area 24), 5x5 (Area 25).
• The 5x5 (Square) provides the largest area.

Section 5:

• Width = 6m (because 48 ÷ 8 = 6)
• Perimeter = 8 + 8 + 6 + 6 = 28m