What You'll Learn
- Perimeter: How to find the total distance around any 2D shape, including compound shapes
- Area Formulas: Calculate areas of rectangles, triangles, trapeziums, and parallelograms
- Compound Shapes: Break complex shapes into simpler ones and add or subtract their areas
- Real-World Problems: Apply area calculations to practical scenarios involving cost and materials
1. Perimeter
What is Perimeter?
Perimeter is the total distance around the outside of a 2D shape. Think of it as walking around the edge of a field — perimeter is how far you'd walk if you went all the way around.
Definition: Perimeter is a length measured in one dimension (mm, cm, m, etc.). For circles, we use the special term circumference instead of perimeter.
Key principle: To find the perimeter of any shape, simply add together the lengths of all its sides.
Perimeter of Regular Shapes
For any regular shape (where all sides are equal), there's a shortcut:
Example: A square with side length 5 cm has perimeter = 4 × 5 = 20 cm.
Why this works: In a regular shape, every side is identical, so you just multiply how many sides there are by the length of one side.
Perimeter of Compound Shapes
A compound shape is made up of two or more simpler 2D shapes joined together. These might be L-shapes, T-shapes, or other irregular forms.
To find the perimeter of a compound shape:
- Identify which sides form the outer edge
- Find any missing side lengths using the properties of shapes
- Add all the outer sides together
Finding missing lengths: In rectangles and parallelograms, opposite sides are equal. In isosceles triangles, two equal sides are marked with dashes. Use these properties to work out missing dimensions.
Finding Perimeter of a Compound Shape
Question: Find the perimeter of this L-shaped compound figure:
┌─────────────────┐
│ 6 cm │
│ ┌──────────┐ │
│ │ │ 2cm
│ │ │ │
4cm│ │ │
│ │ │ │
│ │ │15 cm
│ └──────────┘ │
│ 3 cm 18 cm │
└─────────────────┘
Step 1: Identify which sides are on the outer edge. The dashed lines show the outer perimeter we need to measure.
Step 2: Find missing lengths.
• The top is 6 cm, and the indent is 3 cm, so the right rectangle's width = 6 - 3 = 3 cm
• The full height is 4 cm, and the right part is 2 cm, so the left part's height = 4 - 2 = 2 cm
Step 3: Add all outer sides:
6 + 2 + 3 + (4 - 2) + (6 - 3) + 4 = 6 + 2 + 3 + 2 + 3 + 4 = 20 cm
Q1
A rectangle has length 12 cm and width 8 cm. What is its perimeter?
Q2
2. Area
What is Area?
Definition:
Rectangle Area
Q3
Q4