GM Lesson 026 Areas of Polygons
Learning Intentions
By the end of this lesson, students will be able to:
- Calculate areas of rectangles and triangles.
- Calculate areas of parallelograms and trapeziums.
- Select the correct area formula from the information given.
Prerequisites
Students should already be able to:
- Identify rectangles, triangles, parallelograms and trapeziums.
- Measure and identify base lengths and perpendicular heights.
- Substitute values into a formula.
- Use square units such as
, and . - Distinguish between length units and area units.
Key Idea Summary
Area measures the amount of surface covered by a two-dimensional shape.
The main area formulas for this lesson are:
where
where
where
where
The perpendicular height must be used. A slanted side is not usually the height.
Direct Instruction and Worked Examples
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- Introduction, warmup and vocabulary: 5 minutes
- Direct instruction: 15 minutes
- Understanding checks: 5 minutes
- Exercises: 20 minutes
- Homework: 20 to 30 minutes outside the lesson it was taught in.
Formula Selection
Before calculating an area, identify the shape.
| Shape | Useful Information | Formula |
|---|---|---|
| Rectangle | Length and width | |
| Triangle | Base and perpendicular height | |
| Parallelogram | Base and perpendicular height | |
| Trapezium | Two parallel sides and perpendicular height |
Worked Example 1: Area of a Rectangle
A rectangular garden bed has length
Find its area.
Use:
Substitute:
Calculate:
Therefore, the area is:
Worked Example 2: Area of a Triangle
A triangular sign has base
Find its area.
Use:
Substitute:
Calculate:
Therefore, the area is:
Worked Example 3: Area of a Parallelogram
A parallelogram has base
Find its area.
Use:
Substitute:
Calculate:
Therefore, the area is:
Important: the perpendicular height is used, not the slanted side.
Worked Example 4: Area of a Trapezium
A trapezium has parallel sides of length
Find its area.
Use:
Substitute:
Calculate inside the brackets first:
Therefore, the area is:
Worked Example 5: Selecting the Correct Formula
A shape has two parallel sides of length
Since two parallel sides are given, the shape is a trapezium.
Use:
Substitute:
Therefore, the area is:
Understanding Checks
Check 1
Which formula should be used for a rectangle with length
Check 2
Which formula should be used for a triangle with base
Check 3
A parallelogram has a base of
Which two measurements are needed to calculate its area?
Check 4
A trapezium has parallel sides
What are
Check 5
Explain why area answers use square units.
Exercises
Simple Familiar Exercises
Exercise 1
Find the area of a rectangle with length
Exercise 2
Find the area of a rectangle with length
Exercise 3
Find the area of a triangle with base
Exercise 4
Find the area of a triangle with base
Exercise 5
Find the area of a parallelogram with base
Exercise 6
Find the area of a parallelogram with base
Homework Problems
Homework 1
Find the area of a rectangle with length
Homework 2
Find the area of a triangle with base
Homework 3
Find the area of a parallelogram with base
Homework 4
Find the area of a trapezium with parallel sides
Homework 5
A triangle has area
Find its perpendicular height.
Homework 6
A trapezium has parallel sides
Find its area.
Homework 7
A rectangular courtyard is
A parallelogram-shaped garden bed inside it has base
Find the area of the courtyard not occupied by the garden bed.
Homework 8
A banner is shaped like a trapezium with parallel sides
Find the area of the banner.
Homework 9
A triangular panel has base
Find its area.
Homework 10
Choose the correct formula for each shape and explain why:
- Rectangle with length and width given.
- Triangle with base and perpendicular height given.
- Parallelogram with base and perpendicular height given.
- Trapezium with two parallel sides and perpendicular height given.