GM Lesson 024 Perimeters of Standard Two-Dimensional Objects

Learning Intentions

By the end of the lesson, students will be able to:

• Calculate perimeters of triangles, rectangles, trapeziums and parallelograms.
• Calculate perimeters of composite two-dimensional objects.
• Interpret perimeter calculations in practical situations.

Prerequisites

Students should already be able to:

• Add and subtract whole numbers and decimals.
• Identify triangles, rectangles, trapeziums and parallelograms.
• Recognise that perimeter is measured in linear units such as , , and .
• Identify the outside boundary of a two-dimensional shape.

Key Idea Summary

The perimeter, , of a two-dimensional object is the total distance around its outside boundary.

For standard shapes:

• Triangle:

• Rectangle:

  or

• Parallelogram:

  or

• Trapezium:

For composite shapes:

• Add only the outside edges.
• Do not include internal lines.
• If a side length is missing, use the other given lengths to determine it where possible.
• The final answer must use appropriate linear units.

Direct Instruction and Worked Examples

Time Allocation

Time Allocation

Time Allocation

• 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.

Link to original

Direct Instruction

Perimeter measures length around the boundary of a shape.

It is useful in practical situations such as:

• finding the length of fencing needed around a yard
• finding the length of edging needed around a garden bed
• calculating the amount of trim needed around a sign
• working out the boundary length of a sports court or paved area

Perimeter is NOT area.

• Perimeter measures distance around a shape.
• Area measures space inside a shape.

A useful principle is:

Worked Example 1: Perimeter of a Triangle

A triangular garden bed has side lengths , and . Find its perimeter.

Use:

Substitute:

Calculate:

Therefore, the perimeter is:

Worked Example 2: Perimeter of a Rectangle

A rectangular sign has length and width . Find the length of edging needed to go around the sign.

Use:

Substitute:

Calculate inside the brackets:

Calculate:

Therefore, the length of edging needed is:

Worked Example 3: Perimeter of a Parallelogram

A parallelogram-shaped tile has adjacent side lengths and . Find its perimeter.

Use:

Substitute:

Calculate:

Therefore, the perimeter is:

Worked Example 4: Perimeter of a Trapezium

A trapezium has side lengths , , and . Find its perimeter.

Use:

Substitute:

Calculate:

Therefore, the perimeter is:

Worked Example 5: Composite Perimeter

A composite shape is made from a rectangle with a smaller rectangular section removed from one corner. Its outside boundary has side lengths:

Find the perimeter.

Since the perimeter is the total outside boundary:

Calculate:

Therefore, the perimeter is:

Important: even though the shape is composite, only the outside boundary is counted.

Understanding Checks

Check 1

A rectangle has length and width .

What formula should be used to find its perimeter?

Check 2

A triangle has side lengths , and .

Write the substitution step for its perimeter.

Check 3

A parallelogram has adjacent side lengths and .

Explain why only two side lengths are needed to calculate its perimeter.

Check 4

A composite shape has an internal line drawn across it.

Should the internal line be included in the perimeter calculation? Explain your answer.

Check 5

A student calculates the perimeter of a garden bed and writes the answer as .

Identify the error.

Exercises

Simple Familiar Exercises

Exercise 1

Find the perimeter of a triangle with side lengths , and .

Exercise 2

Find the perimeter of a rectangle with length and width .

Exercise 3

Find the perimeter of a parallelogram with adjacent side lengths and .

Exercise 4

Find the perimeter of a trapezium with side lengths , , and .

Exercise 5

A rectangular garden bed is long and wide. Find the length of edging needed around it.

Complex Familiar Exercises

Exercise 6

A triangular paddock has side lengths , and . Find the length of fencing required to enclose the paddock.

Exercise 7

A parallelogram-shaped paving stone has adjacent side lengths and . Find the total perimeter of identical paving stones.

Exercise 8

A rectangular sports court has length and width . A line is painted around the outside boundary. Find the total length of the painted boundary.

Exercise 9

A trapezium-shaped sign has side lengths , , and . Find the amount of metal trim needed around the sign.

Exercise 10

A composite shape has outside side lengths:

Find its perimeter.

Homework Problems

Problem 1

Find the perimeter of a triangle with side lengths , and .

Problem 2

Find the perimeter of a rectangle with length and width .

Problem 3

Find the perimeter of a parallelogram with adjacent side lengths and .

Problem 4

Find the perimeter of a trapezium with side lengths , , and .

Problem 5

A composite shape has outside side lengths:

Find its perimeter.

Problem 6

A rectangular garden is long and wide. Find the length of fencing needed around the garden.

Problem 7

A parallelogram has perimeter . One side length is . Find the adjacent side length.

Problem 8

A rectangular banner has perimeter . Its length is . Find its width.

Problem 9

A trapezium has perimeter . Three of its side lengths are , and . Find the missing side length.

Problem 10

An L-shaped garden is made by removing a by rectangle from one corner of a by rectangle. Find the perimeter of the L-shaped garden.

Next: GM Lesson 025 Circumference and Sector Arc Length