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1.02 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

ACMEM091

calculate perimeters of familiar shapes, including triangles, squares, rectangles, polygons, circles, arc lengths, and composites of these

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