Rectangle
A = length × width
Learning Objectives
- calculate areas of rectangles, triangles, parallelograms and trapezia;
- identify perpendicular height;
- find areas of combined shapes;
- calculate missing dimensions from area;
- use square units correctly.
Introduction
This lesson develops Area of Plane Shapes from meaning and patterns before moving to calculations. Look for what the quantities, shapes or symbols represent, then connect that idea to the method.
Key Notes
Read the definitions and key facts below carefully. Each rule is most useful when you can explain why it fits the situation, not simply recall it.
Visual Exploration
Notice→Connect→Explain
Use the diagrams, tables or examples in this lesson to identify what changes, what stays fixed and which relationship connects the values.
What Is Area?
Area measures how much flat surface a shape covers.
Key idea: Area counts square units inside a boundary.
Rectangle and Triangle
Triangle
A = ½ × base × perpendicular height
Parallelogram and Trapezium
Parallelogram
A = base × perpendicular height
Trapezium
A = ½(a+b)h, where a and b are parallel sides
Worked Example: Trapezium
Parallel sides are 8 cm and 14 cm, height is 5 cm.
1
A = ½(8+14)×5.
2
A = ½×22×5 = 55 cm².
Combined Shapes
Split a complex figure into familiar shapes, find each area, then add or subtract.
🧠 Let’s Think Together
Before calculating, identify the information given, the result required and the mathematical relationship that connects them. Predict whether the answer should be larger, smaller or unchanged, then use that prediction to check the result.
Practice Questions
Foundation- Find the area of a rectangle 12 cm by 7 cm.
- Find the area of a triangle with base 16 cm and height 9 cm.
- Find the area of a parallelogram with base 11 m and perpendicular height 6 m.
- A trapezium has parallel sides 9 cm and 15 cm and height 8 cm. Find its area.
- A rectangle has area 96 cm² and width 8 cm. Find its length.
- A shape consists of a 10 m by 6 m rectangle and a triangle of base 10 m and height 4 m. Find total area.
- A rectangular garden 18 m by 12 m contains a rectangular pond 5 m by 4 m. Find the area of land outside the pond.
✅ Check Your Work
Show practice answers
- 84 cm²
- 72 cm²
- 66 m²
- 96 cm²
- 12 cm
- 60+20=80 m²
- 216−20=196 m²
Common Mistakes
- Choosing a rule before identifying what the question describes.
- Skipping working or changing notation part-way through a solution.
- Accepting an answer without checking its size, sign or units.
Exam Focus
Show the mathematical relationship you are using, keep notation consistent and give a clear final answer. Use a quick estimate, diagram or inverse operation to check that the result is reasonable.
Summary
- Area uses square units.
- Use perpendicular height.
- Split composite shapes into familiar parts.