1 On the plan of a house, the living room is 3.4 cm long and 2.6cm wide. The scale of the plan
is 1 cm to 2m. Calculate the actual length and width of the room.
Answers
Answer:
Unit 19 Section 2 : Plans
In this section we look at plans drawn to a particular scale.
A scale is used to represent real life measurements on the smaller plan.
Converting measurements
In the example below, we see how to work out "real life" measurements from a plan.
On the left is the plan for a room. The scale for this plan is 1 : 200.
This means that 1 cm on the plan represents 200 cm (or 2 m) in real life.
To work out the dimensions of the room in real life, we need to measure the room on the plan.
The room measures 3 cm by 2 cm.
Because the scale is 1 : 200, the real life measurements will be 200 times larger.
The length of the room in real life must be 3 cm × 200 = 600 cm or 6 m
The width of the room in real life must be 2 cm × 200 = 400 cm or 4 m
Perimeters and Areas
When working out perimeters and areas, it is best to convert to the "real life" measurements first, and then do the calculations.
In the plan above, we worked out that the "real life" dimensions of the room are 6 m by 4 m.
The perimeter of this room must be 6 m + 4 m + 6 m + 4 m = 20 m.
The area of this room must be 6 m × 4 m = 24 m².
Example Question
Below is the plan of a village hall. The scale of the plan is 1 : 100. Use the plan to answer the questions below.
NOTE: You can not measure accurately from the computer screen, so you need to remember that each small square on the plan is half a centimetre wide.
1 cm is the same as the length of 2 small squares.
This will apply for all the questions in this section.
Practice Questions
Work out the answer to each of these questions then click on the button marked Click on this button below to see the correct answer to see whether you are correct.
(a) How long is the kitchen in real life?
(b) What are the dimensions of the main hall in real life?
(c) What is the length of the kitchen window in real life?
(d) What is the perimeter of the main hall in real life?
(e) What is the area of the gents toilet in real life?
Exercises
Work out the answers to the questions below and fill in the boxes. Click on the Click this button to see if you are correct button to find out whether you have answered correctly. If you are right then will appear and you should move on to the next question. If appears then your answer is wrong. Click on to clear your original answer and have another go. If you can't work out the right answer then click on Click on this button to see the correct answer to see the answer.
Remember that 1 cm on each plan is the same as the length of 2 small squares.
Question 1
Below is the plan of a temporary building at a school. It is drawn using a scale of 1 : 100.
(a) What is the actual length of the classroom?
metres
(b) What is the actual width of the classroom?
metres
(c) What are the actual dimensions of the lobby?
Length =
metres
Width =
metres
(d) What are the actual dimensions of the store?
Length =
metres
Width =
metres
Question 2
Adam draws a plan of his bedroom using a scale of 1 : 200.
(a) What is the overall length of his bedroom?
metres
(b) What is the overall width of his bedroom?
metres
(c) What is the width of the narrow part of his bedroom?
metres
(d) What is the perimeter of his bedroom, including the door?
metres
Question 3
Jai's garage is 3 m wide and 8 m long.
Work out the length and width of the garage on a plan with each scale below:
(a) 1 : 100
Width =
cm
Length =
cm
(b) 1 : 200
Width =
cm
Length =
cm
(c) 1 : 50
Width =
cm
Length =
cm
(d) 1 : 10
Width =
cm
Length =
cm
Question 4
On a plan with a scale of 1 : 50, the floor of a rectangular cupboard is shown with dimensions 2.5 cm by 3.6 cm.
What are the actual dimensions of the floor?
Width =
metres
Length =
metres
Question 5
On a plan, an actual length of 5 m is represented by 25 cm.
What is the scale of the plan?
1 :
Question 6
A rectangular room has dimensions 5 cm by 4 cm on a plan with a scale of 1 : 120.
(a) What are the actual dimensions of the room in metres?
Length =
metres
Width =
metres
(b) What is the floor area of the room?
m²
Question 7
The diagram below shows the plan of a room, drawn using a scale of 1 : 200.
(a) What is the perimeter of the room?
metres
(b) What is the floor area of the room?
m²
You have now completed Unit 19 Section 2
Your overall score for this section is
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Produced by A.J. Reynolds January 2001