What is the area of this square in feet?Inside a square, two parallel cuts are made, as shown.  The parallel cuts are 6 inches apart and they partition the square into three regions, all of which...

What is the area of this square in feet?

Inside a square, two parallel cuts are made, as shown.  The parallel cuts are 6 inches apart and they partition the square into three regions, all of which are equal in area.  What is the area of such a square (in square inches)?

Expert Answers
cburr eNotes educator| Certified Educator

kmieciakp is correct about the formula for the area of a square or rectangle. It is Length x Width, NOT 2L + 2W, which is the formula for the perimeter.

I thought it might be useful to explain how you can figure out the length and width in this problem.

You know three things:

1) the large figure is a square, which means all 4 sides are the same length

2) the parallel cuts are 6 inches apart

3) the 3 rectangles made by the cuts are the same area.

We are all assuming that the cuts are parallel to one side of the square, since we don't have the drawing. I think this would have to be the case for the rectangles to be the same.

Since the 3 rectangles are the same area, and they all have a length equal to the length of the square, you can conclude that the width of all three rectangles also has to be the same. We know the distance between the cuts is 6 inches, so all three rectangles have to have a width of 6 inches.

The three rectangles take up the whole area of the big square, so the width of the square has to be 6 + 6 + 6 = 18.

Since the big figure is a square, the length and width have to be the same.

So, the area of the square is 18 inches x 18 inches, which equals 324 square inches.

You did not need to do the conversion into square feet that ladyvols and kmieciakp did -- your problem says the answer should be in square inches.

revolution | Student


Important thing to note:

  1. This figure is the square so all four sides is same in length
  2. Two parallel cuts are make, six inches part
  3. The three rectangular regions, when cut apart in two are equal in area
  4. area of square is length*breadth (mm^2)

Since there is 3 rectangular regions and they are equal in area, we can safely say that the width and the breadth are all similar. The cuts are six inches apart and the rectangles have the same area, so the width of each rectangle is 6 inches.

As you know there is 3 rectangles which make up the square, and each of their width is 6 inches, so the width of the square is 6*3= 18 inches.

As this is the square, the width and the length is the same, so the area is:

area of square= 18^2= 324 inches square.

kmieciakp | Student

I thought area was length times width (LxW)--isn't 2L+2W the formula for the perimeter?

So 18 inches times 18 inches = 144+180=324 square inches

1.5 feet times 1.5 feet = .75+1.50 = 2.25 square feet

Okay, yes--I'm pretty sure that's right--let's see if the answers are the same:

To convert 2.25 square feet to square inches, you'd multiply the square feet (2.25) by the number of inches in a foot squared.  So, 2.25 times 12 squared would be 2.25 times 144, which works out to 324 square inches.

So, to answer your question, the area in square feet is 2.25 square feet.