November:

Perimeters, Areas, & Volume

Designing A Floor Plan

You are in charge of setting up a floor plan of a family room. The room measures 20 x 17 feet, but use this 20 x 17 square centimeter grid to arrange your model floor plan.

Your job as an interior decorator is to best organize the room with all of the following furniture items. The area measure of each furniture item is given in centimeters.

  1. Lamp Table - 4 cm2
  2. Sofa - 24 cm2
  3. Coffee Table - 10 cm2
  4. End Tables (2) - 2cm2 each
  5. Computer Desk - 12 cm2
  6. Bookcase - 12 cm2
  7. Big Screen TV - 8 cm2
  8. Stero - 14 cm2
  9. Arm Chair (2) - 9cm2 each
  10. Pool Table - 36cm2
  11. Plant Stands (2) - 4cm2 each
  12. Computer Chair - 4 cm2

What's the Big Idea?

Your goal is set up the family room in a comfortable and practical way that would provide the maximum amount of walk space for the room. The furniture items can be designed in any polygonal shape as long as each furniture's area remains the same. For example: the bookcase (area = 12 cm2) can be 3 x 4, or 2 x 6, or 12 x 1, or a polygon measuring 12 cm2.

Here is one sample of how you can arrange the floor pattern.

Let's Give It A Try !

Use two copies of the family room grid (20 x 17) to explore the many different ways to design the room. You'll use one grid to design the furniture and the other grid to set up the room.
Here are some ideas to think about as you devise your plan.

What is the total area of the family room? (in cm2 or ft2)

What is the total area of all the furniture items put together?

How can you design the computer chair so that it is shaped not like a square? (remember to keep the area to exactly 4cm2)

If you design the pool table (area = 36cm2) in a 3 x 12 shape, would its perimeter be larger, smaller or equal to a shape of 4 x 9 or even 6 x 6? Would this concept be important to setting up your family room?

If you had to pack up the Big Screen TV (height of 4ft), what size packing box would you need to get? What would the volume of the box be? Would the volume depend on the how you designed the area of the TV?

Results:

After you finish designing your furniture and arranging the family room, explain what you did to complete your task.
What worked and what didn't work? Why?
What is the total area of available of the walking space ?
How did the concepts of area and perimeter help you?

Spread The News!

Send us your floor plan designs or email us your results.

We hope to have our class' samples posted soon!

September:
Math Fun With Spirolaterals		 October:
Exploring Number Patterns
November:
Perimeter, Area, & Volume		 December:
Toy Story Math

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