Lesson 2: Constructing Similar Polygons - Floor Plans

   Constructing Knowledge

As discussed earlier in this lesson, a floor plan is a scale diagram used by people who work in fields such as interior design or construction. Software programs are frequently used to improve the efficiency of creating floor plans.

In this course, you have developed the skills required to create a floor plan without the assistance of a software program.

When creating a floor plan, keep in mind the following:

  • Floor plans for this course are from a viewpoint above the room, looking down.
  • The scale factor used to go from the size of a room to the size of a piece of paper is your choice, so choose a scale factor that is easy to work with.
  • The unit of measure (cm or inches) needs to stay the same for all measurements.
  • List all items in the room with original dimensions and reduced dimensions
  • Using grid paper can reduce the amount of measuring needed.
  • Doors typically swing into a room. Be careful not to block a doorway.

EXAMPLE 1

Harper is reorganizing a small rectangular living room in his home. The room is 5 metres by 4 metres. The room has 1 couch, 1 love seat, a recliner, two coffee tables, a bookshelf and an entertainment stand. Draw one possible arrangement of the room on a standard sheet of 1 cm grid paper. The dimensions of each piece of furniture are listed below.

Item Original dimensions
couch 210 cm × 90 cm
love seat 165 cm × 90 cm
coffee table 1 120 cm × 60 cm
coffee table 2 60 cm × 60 cm
recliner 100 cm × 100 cm
entertainment stand 130 cm × 50 cm
bookshelf 90 cm × 30 cm

Solution


Step 1: Establish a scale

The first step in this type of problem is to establish a scale. A standard sheet of paper is 8 in by 11.5 in, or approximately 29 cm by 20.3 cm.

Converting the room size to centimetres will allow the rest of the problem to be solved in centimetres.
4 m = 400 cm
5 m = 500 cm

Picking a scale factor can be done with a guess and check strategy:

Factor to reduce by Reduced dimensions of room Does it fit a 29 cm by 20 cm piece of paper?
5 500 cm ÷ 5 = 100 cm
400 cm ÷ 5 = 80 cm

100 cm by 80 cm 		No. These dimensions are still too large.
10 500 cm ÷ 10 = 50 cm
400 cm ÷ 10 = 40 cm

50 cm by 40 cm 		No. These dimensions are still too large.
20 500 cm ÷ 20 = 25 cm
400 cm ÷ 20 = 20 cm

25 cm by 20 cm 		Yes. These dimensions will fit almost perfectly.

Step 2: Reduce the dimensions of all items in the room by the chosen scale factor.

To draw a floor plan of the room, the dimensions of the room and all of its furniture must be reduced by a factor of 20. This means each set of dimensions will need to be divided by 20 to get the new dimensions for the floor plan.

Item Original dimensions Floor plan dimensions
couch 210 cm × 90 cm 10.5 cm × 4.5 cm
love seat 165 cm × 90 cm 8.25 cm × 4.5 cm
coffee table 1 120 cm × 60 cm 6 cm × 3 cm
coffee table 2 60 cm × 60 cm 3 cm × 3 cm
recliner 100 cm × 100 cm 5 cm × 5 cm
entertainment stand 130 cm × 50 cm 6.5 cm × 2.5 cm
bookshelf 90 cm × 30 cm 4.5 cm × 1.5 cm

Step 3: Place the furniture in the room.

Counting squares on the grid paper instead of using a ruler can make drawing each item easier. Either method will give accurate results. The grid drawn is 25 by 20 to correspond to the room size.



Solution


Another strategy for placing the items in the room is to use a second sheet of grid paper and make scale cut outs of each of the pieces of furniture. Once the cutouts are made, they can be moved around until placement is finalized. Once the placement is finalized, they can be drawn onto the diagram. Using a single sheet may lead to lots of drawing and erasing.


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