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2.02 Perimeter

Worksheet
Triangles, rectangles, squares and other polygons
1

Find the perimeter of the following squares:

a
b
c
d

A square with side length 6\text{ cm}.

e

A square with side length 9.1\text{ m}.

2

Find the perimeter of the following rectangles:

a
b
c
d
e
3

Find the perimeter of a rectangle with a length of 4\text{ m}, and a width of 23\text{ m}.

4

Find the perimeter of the following triangles:

a
b
c
d
e
f
5

Find the perimeter of the following triangles:

a

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

b

An isosceles triangle where the 2 equal side lengths are 16\text{ mm} each and the third side of length 4\text{ mm}.

6

Find the perimeter of a regular pentagon with side length 9 metres.

7

Find the perimeter of the following quadrilaterals:

a
b
c
d
e
8

Find the perimeter of the regular hexagon shown:

9

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}.

10

Find the missing dimension of the following rectangles:

a
b
c
11

Find the length of a rectangle with a perimeter of 42\text{ cm} and width of 7\text{ cm}.

12

Find the side length of the following squares:

a
b
c

A square with a perimeter of 16\text{ mm}.

d

A square with a perimeter of 12\text{ mm}.

13

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

14

A triangle has a perimeter of 29\text{ m} and two sides of lengths 8\text{ m} and 8\text{ m}. Find the length of the third side.

15

Find the missing side length of the following triangles:

a
b
c
d
16

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

Composite shapes
17

Find the perimeter of the following figures:

a
b
c
d
18

For each of the following figures:

i

Find the length x.

ii

Find the length y.

iii

Find the perimeter.

a
b
19

Consider the following figure:

a

Find the length x.

b

Find the length y.

c

Find the length z.

d

Find the perimeter of the figure.

Applications
20

A backyard is in the shape as shown:

What is the total length of its boundary?

21

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?

22

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

23

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:

a

What are the dimensions of the pool without the path around it?

b

What is the perimeter of the pool?

24

A present is contained in a cube shaped box. Ribbon is wrapped around the present as shown 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. How much ribbon is needed altogether to wrap around the box once and do a bow?

c

What is the total length of ribbon needed if we wrap the present with two lengths of ribbons? Assume a single bow is tied.

25

Calculate the perimeter in metres of the plot of land pictured below on the site plan, if all measurements are given in metres.

26

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.

27

An outline of a block of land is shown:

a

Calculate the perimeter of the land.

b

Fencing costs \$32 per metre. Calculate the fencing cost for this block of land.

28

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 is the length of the fence?

b

Fencing costs \$47 per metre. Calculate the fencing cost, to the nearest dollar for this block of land.

29

In the following diagram, each square of the grid has a side length of 30\text{ m}. A jogger runs the perimeter of the park 4 times each morning.

a

What is the distance of one lap of the park?

b

How far will the jogger run each week? Give your answer in kilometres.

30

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?

31

Find the length of wire needed to create the frame of the following rectangular prism:

32

Consider the frame shown:

Note that the three triangles formed are equilateral and lie parallel to each other and perpendicular to the vertical tubes, of which there are six of length 3.99\text{ m}.

a

What is the length of tubing needed to create this frame?

b

If the tubing costs \$7.16 per metre, what is the cost to make the frame?

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Outcomes

3.1.2.1

use metric units of length (millimetres, centimetres, metres, kilometres), their abbreviations (mm, cm, m, km), conversions between them, and appropriate levels of accuracy and choice of units

3.1.2.3

use formulas to calculate perimeters of familiar shapes, including triangles, squares, rectangles, polygons, circles and arc lengths

3.1.2.4

use formulas to calculate perimeters of familiar composite shapes [complex]

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