# 4.02 Perimeter

Worksheet
Triangles and rectangles
1

What is the perimeter of a polygon?

2

Find the perimeter of the following:

a
b
c
d
3

Find the perimeter of the following:

a

A square if each side is 6\text{ cm} long.

b
A square if each side is 9.1\text{ m} long.
c

A rectangle with length 4 \text{ m} and width 23 \text{ m}.

d

A rectangle whose length is 17\text{ cm} and width is 8\text{ cm}.

4

Find the perimeter of the following:

a
b
5

Find the perimeter of the following:

a

A scalene triangle with side lengths 15 \text{ mm}, 19 \text{ mm}, and 22 \text{ mm}.

b

An isosceles triangle where the two equal side lengths are 16 \text{ mm} each and the third side length is 4 \text{ mm}.

6

Find the perimeter of the following parallelograms:

a
b
c
7

Find the perimeter of the following kites:

a
b
c
8

Find the perimeter of the following trapeziums:

a
b
9

Find the perimeter of the rhombus shown:

10

Find the perimeter of the following figures:

a
b
Regular polygons and composite shapes
11

Find the perimeter of the regular hexagon shown:

12

Find the perimeter of the following:

a

A regular pentagon with side length 8 \text{ cm}.

b

A regular hexagon with side length 20 \text{ m}.

c

A regular octagon with side length 7 \text{ mm}.

d

A regular 20-sided shape with side length 4 \text{ cm}.

13

For each of the figures below, find:

i

x

ii

y

iii

The perimeter

a
b
14

Consider the following figure:

a

Find the value of x.

b

Find the value of y.

c

Find the value of z.

d

Find the perimeter.

15

Find the perimeter of the following figures:

a
b
c
d
Unknown sides
16

Find the missing side length of the following quadrilaterals:

a
b
c
d
e
f
g
17

A rectangle has a perimeter of 42 \text{ cm}. If its width is 7 \text{ cm}, find the length of the rectangle.

18

A square has a perimeter of 16 \text{ mm}. Find the side length of the square.

19

Find the side length of a rhombus if its perimeter is 24\text{ mm}.

20

Find the value of y in the diagram, if the perimeter of the triangle is 29 \text{ m}.

21

Find the value of d in the diagram, if the perimeter of the triangle is 35 \text{ cm}.

22

Find the side length of an isosceles triangle with a perimeter of 29 \text{ m}, given that the other two sides both have a length of 8 \text{ m}.

23

The following pentagon has a perimeter of 20 m. Find the length of each side.

24

Find the side length of a regular hexagon with a perimeter of 96\text{ m}.

25

A square has the same perimeter as an equilateral triangle. If the triangle has sides of length 12\text{ cm}, find the side length of the square.

Applications
26

Sandy wants to build a thin wire frame for a photo that is 12\text{ cm} long and 5\text{ cm} wide. What length of wire will she need to go around the entire photo?

27

A rectangular athletics field is 140 \text{ m} long and 40 \text{ m} wide. How far, in kilometres, will an athlete run by completing 6 laps along the edge of the field?

28

A swimming pool has a 3\text{ m} wide path around its edge. The outer width of the path is 15 \text{ m} and the length is 29 \text{ m}, as shown in the diagram:

a

Find the dimensions of the pool.

b

Find the perimeter of the pool.

29

A present is contained in a cube shaped box. Ribbon is wrapped around the sides as shown in the first diagram below:

a

If the side length of the box is 10\text{ cm}, what is the shortest length of the ribbon needed to neatly go around the box without overlap?

b

The bow requires 8\text{ cm} of ribbon. What length of ribbon is needed in total?

c

What is the total length of ribbon needed if we wrap the present with two lengths of ribbon, as shown in the second diagram? Assume a single bow is tied.

30

Calculate the perimeter in metres of the plot of land pictured here on this site plan. All measurements are given in metres.

31

A fence is to be constructed around a rectangular building site measuring 17 \text{ m} by 26 \text{ m}. Find the cost of constructing the fence at \$26 per metre. 32 An outline of a block of land is pictured below: a Calculate the perimeter. b Fencing costs \$32 per metre. Calculate the fencing cost for this block of land.

33

A rectangular block of land is 25\text{ m} long and 12\text{ m} wide. A fence is to be constructed around the perimeter.

a

What length of fence is required?

b

Fencing costs \$47 per metre. Calculate the fencing cost, to the nearest dollar, for this block of land. 34 Calculate the length of wire Luke will need if he is making a frame in the shape of the following triangular prism: 35 Find the length of wire needed to create the frame of the following rectangular prism: 36 The frame shown is made up of three equilateral triangles that lie horizontally and three vertical tubes of equal length. The triangles are equally spaced along the vertical tubes: a Find the length of tubing needed to create the entire frame. b If the tubing costs \$7.16 per metre, find the cost to make the frame.

37

Buzz walks at an average speed of 4 \text{ km/hr} while checking the fence around his farm. The farm is square in shape and has a side length of 16 \text{ km}. How long will it take Buzz to check the fence?

### Outcomes

#### 1.3.1

choose and use appropriate metric units of length, their abbreviations, conversions between them, and appropriate levels of accuracy, such as mm for building and other trade contexts, cm for textiles

#### 1.3.3

convert between metric units of length and other length units for simple practical purposes, for example, 1 inch ≈ 2.54cm

#### 1.3.4

calculate perimeters of familiar shapes, including: triangles, squares, rectangles and composites of these