Scale Drawing (HSC SSCE Mathematics Standard): Revision Notes

Scale Drawing, Plans, and Elevations

What is a scale drawing?

A scale drawing represents a real object at a different size, usually smaller, to make it easier to work with on paper. The most common example of a scale drawing is a map, which shows a large area like a country or city in a size that fits on a page.

The scale factor is the ratio that compares the size of the drawing to the actual size of the object. For instance, on a map, $1$ cm on the paper might represent $1$ km in real life.

Two ways to express scale

Scale can be written in two different ways:

1. Using units: For example, $1$ cm to $1$ m or $1$ cm $=$ $1$ m
   • This tells you directly what measurement on the drawing represents in reality
   • The first measurement is always the drawing size
   • The second measurement is always the actual size
2. Using a ratio (no units): For example, $1:100$
   • This means the actual distance is $100$ times the drawing distance
   • Both measurements must be in the same units
   • The ratio $1:100$ means $1$ unit on the drawing equals $100$ units in reality

Key formula:

$\text{Scale of a drawing} = \text{Drawing length} : \text{Actual length}$

Working with scales

When working with scale drawings, you need to convert between the drawing measurements and the actual measurements.

Finding the actual length

To find the actual length when you know the drawing length:

• Multiply the drawing length by the scale factor

Finding the drawing length

To find the drawing length when you know the actual length:

• Divide the actual length by the scale factor

Plans and elevations

When creating technical drawings, we often need to show different views of a three-dimensional object. The two main types of views are plans and elevations.

Plan view

A plan is the view of an object from directly above, looking down on it. For buildings, a floor plan is a horizontal section cut through the building that shows:

• Walls and their thickness
• Windows and doors
• Door openings and which way doors swing
• Fittings and appliances (like toilets, sinks, bathtubs)
• Room layouts and sizes

Elevations

An elevation is the view of an object from one side. Common types include:

• Front elevation: The view from the front of the object
• Side elevation: The view from the side of the object

For buildings, elevations are vertical sections parallel to one side of the building. They show what the building looks like from different directions, including features like windows, doors, roof shape, and external details.

Building plans

Floor plans are a practical and important use of scale drawings. They allow architects, builders, and homeowners to see the layout of a house and calculate dimensions.

Understanding floor plans

Building plans typically use a scale such as $1:150$. This means:

• Every $1$ cm on the floor plan represents $150$ cm (or $1.5$ m) in the actual building
• You can measure the plan with a ruler and multiply by $150$ to find real dimensions

Common floor plan symbols

Floor plans use standard symbols to represent different features. Here are the most common ones:

Learning these symbols helps you quickly read and understand floor plans.