 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