Example 1
Find the area of a rectangle 7 cm long and 4 cm wide.
- For a rectangle, area = length × width.
- Multiply 7 by 4.
- 7 × 4 = 28
So: The area is 28 cm².
Back to National 4
Topic
Geometry and Practical Measure
Area measures the space inside a 2D shape. It is used for floors, walls, fields, tiles, and compound shapes.
Topic explanation
Area is measured in square units such as cm² or m² because it counts squares covering a surface.
For triangles and parallelograms, use the perpendicular height, not a sloping side.
Compound shapes become easier when you split them into rectangles, triangles, or other familiar shapes.
Quick methods
- Rectangle
- Area = length × width
- Triangle
- Area = base × height divided by 2
- Parallelogram
- Area = base × perpendicular height
- Compound shapes
- Split into simple shapes, then add or subtract areas.
Worked examples
Example 2
Find the area of a triangle with base 10 cm and height 6 cm.
- For a triangle, area = base × height divided by 2.
- Multiply the base and height: 10 × 6 = 60
- Divide by 2: 60 divided by 2 = 30
So: The area is 30 cm².
Example 3
A compound shape is made from rectangles measuring 8 m by 3 m and 5 m by 4 m. Find the total area.
- Find the first rectangle area: 8 × 3 = 24 m².
- Find the second rectangle area: 5 × 4 = 20 m².
- Add the areas: 24 + 20 = 44
So: The total area is 44 m².