085r. Perimeter of 2D Shapes

Learning Intentions

• To understand that perimeter is the distance around the outside of a two-dimensional shape
• To understand that marks can indicate two (or more) sides are of equal length
• find the perimeter of a shape when the measurements are given

Pre-requisite Summary

• Know that length is measured in units such as mm, cm, m and km
• Know that a two-dimensional shape is flat and has sides around its boundary
• Know how to add whole numbers and decimals
• Know that the perimeter of a shape is found by adding the lengths of its outside edges
• Know that equal side marks show sides that have the same length
• Know that if one marked side has a measurement, all sides with the same mark have that measurement

Worked Examples

Worked Example 1

Find the perimeter of each shape.
a) A square with side length $6\text{ cm}$
b) A rectangle with length $9\text{ cm}$ and width $4\text{ cm}$

Worked Example 2

A triangle has side lengths $5\text{ cm}$, $7\text{ cm}$ and $8\text{ cm}$. Find its perimeter.

Worked Example 3

A rectangle has one long side labelled $11\text{ m}$ and one short side labelled $3\text{ m}$. Equal side marks show opposite sides are equal. Find the perimeter.

Worked Example 4

An isosceles triangle has two equal sides marked. One of the equal sides is $6\text{ cm}$ and the third side is $9\text{ cm}$. Find the perimeter.

Worked Example 5

A pentagon has side lengths $4\text{ cm},4\text{ cm},6\text{ cm},3\text{ cm}$ and $3\text{ cm}$. Equal side marks show the matching lengths. Find the perimeter.

Worked Example 6

An L-shaped figure has outside side lengths $8\text{ cm},5\text{ cm},3\text{ cm},2\text{ cm},5\text{ cm}$ and $6\text{ cm}$. Find the perimeter.

Problems

Problem 1

Find the perimeter of each shape.
a) A square with side length $8\text{ cm}$
b) A rectangle with length $10\text{ cm}$ and width $5\text{ cm}$

Problem 2

A triangle has side lengths $6\text{ cm}$, $9\text{ cm}$ and $10\text{ cm}$. Find its perimeter.

Problem 3

A rectangle has one long side labelled $14\text{ m}$ and one short side labelled $5\text{ m}$. Equal side marks show opposite sides are equal. Find the perimeter.

Problem 4

An isosceles triangle has two equal sides marked. One of the equal sides is $7\text{ cm}$ and the third side is $11\text{ cm}$. Find the perimeter.

Problem 5

A pentagon has side lengths $5\text{ cm},5\text{ cm},7\text{ cm},4\text{ cm}$ and $4\text{ cm}$. Equal side marks show the matching lengths. Find the perimeter.

Problem 6

An L-shaped figure has outside side lengths $9\text{ cm},4\text{ cm},3\text{ cm},2\text{ cm},6\text{ cm}$ and $7\text{ cm}$. Find the perimeter.

Exercises

Understanding and Fluency

1. Decide whether each statement describes perimeter.
   a) The distance around the outside of a shape
   b) The amount of space inside a shape
   c) Adding all outside side lengths

2. Find the perimeter of each shape.
   a) A square with side length $4\text{ cm}$
   b) A square with side length $9\text{ cm}$
   c) A square with side length $12\text{ cm}$

3. Find the perimeter of each rectangle.
   a) Length $7\text{ cm}$, width $3\text{ cm}$
   b) Length $11\text{ m}$, width $2\text{ m}$
   c) Length $8.5\text{ cm}$, width $4\text{ cm}$

4. Find the perimeter of each triangle.
   a) Sides $3\text{ cm},4\text{ cm},5\text{ cm}$
   b) Sides $6\text{ cm},6\text{ cm},9\text{ cm}$
   c) Sides $10\text{ m},7\text{ m},8\text{ m}$

5. Equal side marks show some sides are the same length. Find each perimeter.
   a) A rectangle with one side $12\text{ cm}$ and an adjacent side $5\text{ cm}$
   b) An isosceles triangle with equal sides $8\text{ cm}$ and third side $6\text{ cm}$
   c) A kite with side lengths $4\text{ cm},4\text{ cm},7\text{ cm},7\text{ cm}$

6. Find the perimeter of each shape.
   a) A pentagon with side lengths $2\text{ cm},3\text{ cm},4\text{ cm},5\text{ cm},6\text{ cm}$
   b) A hexagon with all sides $3\text{ cm}$
   c) A quadrilateral with side lengths $9\text{ cm},6\text{ cm},9\text{ cm},6\text{ cm}$

7. Find each perimeter.
   a) A shape with sides $15\text{ mm},10\text{ mm},15\text{ mm},10\text{ mm}$
   b) A triangle with sides $12.5\text{ cm},12.5\text{ cm},9\text{ cm}$
   c) A rectangle with sides $2.4\text{ m}$ and $1.6\text{ m}$

8. An object does not start at zero on a ruler. Its side lengths are measured as $5\text{ cm},3\text{ cm},5\text{ cm}$ and $3\text{ cm}$. Find the perimeter.

Reasoning

9. Explain why perimeter is found by adding side lengths, not by multiplying all of them together.

10. A student says that equal side marks are just decoration and do not affect the calculation. Explain why this is incorrect.

11. A rectangle has one side labelled $8\text{ cm}$ and one adjacent side labelled $3\text{ cm}$. Explain how equal side marks help you know the lengths of the other two sides.

12. A student finds the perimeter of a triangle with sides $5\text{ cm},5\text{ cm},8\text{ cm}$ by doing $5+8=13$. Describe the mistake.

Problem-solving

13. A garden bed is rectangular with length $14\text{ m}$ and width $6\text{ m}$. How much edging is needed to go all the way around it?

14. A picture frame is a square with side length $22\text{ cm}$. What is its perimeter?

15. A triangular sign has two equal sides of $9\text{ cm}$ and a base of $12\text{ cm}$. Find the perimeter.

16. A running track is made in the shape of a rectangle with length $120\text{ m}$ and width $50\text{ m}$. How far is one lap around the outside?

17. A pentagonal badge has side lengths $3\text{ cm},4\text{ cm},4\text{ cm},6\text{ cm}$ and $6\text{ cm}$. Find its perimeter.

18. A floor plan shows an L-shaped room with outside side lengths $7\text{ m},4\text{ m},2\text{ m},3\text{ m},5\text{ m}$ and $4\text{ m}$. What is the perimeter of the room?

Potential Misunderstandings

• A student may confuse perimeter with area and think perimeter measures the space inside a shape
• A student may add only some of the side lengths instead of all outside edges
• A student may ignore equal side marks and treat unlabelled matching sides as unknown
• A student may think equal side marks mean the sides are parallel rather than equal in length
• A student may use the same number twice incorrectly, even when side marks do not show equality
• A student may forget to include all outer sides of a composite shape such as an L-shape
• A student may make arithmetic errors when adding several side lengths
• A student may leave the answer without units or use the wrong unit

Next: 086e. Radius, Diameter and Circumference of Circles