Perimeter, Area & Volume
Learn to measure the distance around shapes, the space inside flat shapes, and the space inside 3D objects.
Perimeter
The perimeter is the total distance around the outside of a shape. To find the perimeter, add up all the side lengths.
Rectangle Perimeter
Perimeter = 8 + 5 + 8 + 5 = 26 cm
Or use the formula: P = 2 × (length + width) = 2 × (8 + 5) = 2 × 13 = 26 cm
Compound Shape Perimeter
Add all outer edges: 10 + 5 + 5 + 5 + 5 + 10 = 40 cm
For compound shapes, trace around the outside and add every edge length.
Area
Area is the amount of space inside a 2D shape. We measure area in square units (cm², m²).
Concrete: Counting Grid Squares
Count the squares inside the shape to find the area.
5 columns × 3 rows = 15 square units
Pictorial & Abstract: The Formula
Area of a Rectangle = Length × Width
A = L × W
Volume
Volume is the amount of space inside a 3D object. We measure volume in cubic units (cm³, m³).
3D Rectangular Prism (Cuboid)
Volume = Length × Width × Height
V = L × W × H
V = 4 × 2 × 3 = 24 cm³
Think of it as 24 little unit cubes stacked inside the box.
Concrete: Counting Unit Cubes
Imagine building with unit cubes. Each layer has L × W cubes. Stack H layers.
1 layer = 4 × 2 = 8 cubes
Key Vocabulary
Perimeter
The total distance around the outside of a shape. Measured in cm, m, etc.
Area
The amount of surface inside a 2D shape. Measured in square units (cm²).
Volume
The amount of space inside a 3D object. Measured in cubic units (cm³).
Compound Shape
A shape made by combining two or more simple shapes (like an L-shape).
Worked Examples
Find the perimeter of a rectangle with length 12 cm and width 7 cm.
Step 1: Use the formula: P = 2 × (L + W)
Step 2: P = 2 × (12 + 7) = 2 × 19
Answer: Perimeter = 38 cm
Find the area of a rectangle 6 cm long and 4 cm wide.
Step 1: Use the formula: A = L × W
Step 2: A = 6 × 4
Answer: Area = 24 cm²
Find the volume of a box that is 5 cm long, 3 cm wide, and 2 cm high.
Step 1: Use the formula: V = L × W × H
Step 2: V = 5 × 3 × 2
Answer: Volume = 30 cm³
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
What is the perimeter of a rectangle with length 10 cm and width 4 cm?
Question 2
What is the area of a rectangle that is 7 cm long and 5 cm wide?
Question 3
What is the volume of a box that is 6 cm long, 4 cm wide, and 3 cm high?
Question 4
A square has a perimeter of 36 cm. What is the length of one side?
Question 5
A rectangular garden is 8 m long and 5 m wide. What is its area?
Key Concepts Summary
- ●Perimeter = total distance around a shape (add all sides).
- ●Area of a rectangle = Length × Width (measured in cm², m²).
- ●Volume of a rectangular prism = Length × Width × Height (measured in cm³, m³).
- ●For compound shapes, break them into simpler rectangles.
- ●Always check your units: cm for perimeter, cm² for area, cm³ for volume.