4.07 Scales and maps

So far we have used ratios in a wide range of contexts, but they are particularly useful in scale drawings. To create maps, building plans, and other technical drawings, the features being represented must be scaled down to fit on the piece of paper, and we express this scaling factor with a ratio. For example, if a small city is $100000$100000 times larger than a piece of paper, scaling its features down onto a map drawn on that paper would have the scaling ratio of $1:100000$1:100000, meaning $1$1 cm measured on the map represents $100000$100000 cm (or $1$1 km) in real life.

Another way to represent the distances on a map or building plan is to use a scale bar. This small bar on the drawing shows the corresponding distance in real life. On a map, a scale bar might measure $10$10 cm long, but if it is labelled as $20$20 km we know that if two features are $10$10 cm apart on the map then they are $20$20 km apart in real life.

The following table shows some common abbreviations used on floor plans: 
 

Abbreviation	Meaning
CAB	Cabinet
CBD/CPD	Cupboard
D	Door
KIT	Kitchen
LIN	Linen Cupboard
O	Oven
R/REFRIG	Refrigerator
SD	Sliding door
SHR	Shower
TV	Television
W	Window
WC	Water closet (bathroom)
WR	Wardrobe

 

 

Exploration

A floor plan or building plan is a scaled down representation of a building, including walls, windows, doors, stairs, and other fixtures. This floor plan has a scale bar to determine the true distances between objects. The scale bar represents $2$2 m.

 

The distance between the sink and the dining room table is approximately $3$3 lengths of the scale bar. So the distance between them is $3\times2$3×2 m , or $6$6 m. We can also identify certain rooms by their fixtures. The room in the top left is the kitchen corner as it contains a pantry, oven, sink and stove top.

Rooms that contain a shower, toilet, bathtub and sink can be easily identified as the bathroom or ensuite. An example of such a bathroom is given in the top right of the following floor plan.

Some symbols may be less intuitive than others. Here are some of the most common symbols used in floor plans - there may be others used depending on the architect, but they are often easy to guess.

Fixture	Door	Window	Wall	Stairwell	Shower	Toilet	Sink	Towel rack	Stovetop	Oven
Symbol

 

Here is the same building plan, but instead of a scale bar the true lengths of objects are given in centimetres:

We can use these lengths to find the dimensions of different rooms, so for example the internal dimensions of the bathroom will be $695$695 cm$\times$×$410$410 cm. Using internal dimensions means that measurements do not include the width of the walls.

This is the elevation view of the building, meaning we are looking at it side-on rather than top-down:

If we want to find $A$A, the width of the building, we need to first figure out which wall is shown in the elevation view by matching its features with the correct wall of the floor plan.

The side of the building we want to measure has a single window and a single door, and according to the floor plan there is only one wall that has both a window and a door - the northern wall. The width of the northern wall is not labelled on the floor plan, but we can tell that it has the same width as the the southern walls added together:

Width	$=$=	$25+550+25+680+25$25+550+25+680+25	(adding the lengths labelled on the southern wall)
	$=$=	$1350$1350 cm	(simplifying the addition)

So the width of the southern wall and northern wall are both $1350$1350 cm. In other words, $A=13.5$A=13.5 m.

 

With a scale bar or a scale ratio we can always accurately determine the real life dimensions of the building or territory from the scale drawing or map, so look for that information first.

Practice questions

question 1

question 2

question 3