Solve & discuss it!

Question

Adama and his dad are building a tree house. They buy enough flooring material to cover the area of 36 square feet. What are all the possible dimensions of the floor?

Answer 1

If the tree house is rectangular, then the dimensions can be x and 36/x for any x between 0 and 36. For example,

x=6: dimensions 6 by 6

x=2.5: dimensions 2.5 by 14.4

x=5: dimensions 5 by 7.2

x=π: dimensions π ≈ 3.14 by 36/π ≈ 11.5

and so on.

But the tree house might have another shape. It could have a circular platform to the side of the tree trunk. In that case, the area of the circle is π·r² = 36. Solving for r gives r=6/√pi ≈ 3.4.

If the tree house is circular, then more likely it encircles the tree, with a hole in the floor for the trunk to pass through. Suppose the hole in the floor has a diameter of 1 foot, and the circular floor has a diameter of r feet. Then the floor area is π·r² - π·1² = 36. Solving for r, we get r=√(36/π + 1) ≈ 3.5.

You can find dimensions for other shapes as well, like a hexagon, trapezoid, rhombus, star...

Answer 2

I have worked out the problem on this whiteboard for your review. Since the area of a space is the length x width, you will need to find all pairs of multiples that equal 36. I hope this helps. Let me know if you have any additional questions. Take care

Dr. Christal-Joy Turner

Answer 3

2 x 18 = 36

3 x 12 = 36

4 x 9 = 36

6 x 6 = 36

And that is just some of the whole numbers!