1. Section 2

1.18. Explore 3

Mathematics 20-3 Module 5

Section 2: Perspective and Scale

 

Try This 3

 

Sometimes on a map, instead of a ratio such as 1:125 000, the scale is expressed as 1 cm = 1.25 km. If this is the case, think about how this data might change the calculation.

  1. Set up the proportion you would use. Check hint

  2. Solve the proportion to find the actual distance. Check hint

Scale is used on maps, blueprints, mechanical drawings, microscopic diagrams, model planes and trains, and photography. Now that you have been introduced to scale, it’s time for you to draw scale diagrams of some everyday two- and three-dimensional objects.

 

This is a photo of an antique trunk.

Comstock/Thinkstock

Example

 

An antique trunk is 40 cm wide, 100 cm long, and 60 cm high. Draw a scale diagram of this trunk on 1-cm isometric paper.

 

Solution

 

The trunk is 40 cm wide, 100 cm long, and 60 cm high.

  1. Choose a scale.

    • If 1 cm on the isometric paper is equal to 10 cm for the actual trunk, the scale is 1:10.

  2. Set up proportions using the scale 1:10 to find the length of each side in the scale drawing.

    • Width of trunk in scale drawing:



    Note: You may notice at this point that the actual length of 40 cm is divided by 10 to find the scale drawing length of 4 cm. To find the remaining lengths, use this shortcut.

    • Length of scale diagram = 100 cm ÷ 10 = 10 cm.
    • Height of scale diagram = 60 cm ÷ 10 = 6 cm.

  3. Draw the 3-D isometric image.

    This is a graphic of an isometric diagram six centimetres high, four centimetres wide, and ten centimetres long.

    • Draw the height (shown in black) 6 cm high. This will be one corner of the box.

    • Draw the width (shown in red) 4 cm long.

    • Draw the length (shown in green) 10 cm long.

    • Then complete the 3-D image of the trunk.