Friday, September 21, 2012

Planning Out Your Floor

Charlie is helping his family design a sun porch for their house. It will be in the shape of a trapezoid (ABCD), allowing for large windows on several sides. Charlie has labeled the four corners A, B, C, and D. He wants to find out how many 12-inch-square floor tiles he should order if 2 dozen extra tiles are needed for replacements or cutting errors. The tiles come in boxes of 12 tiles per box.

Following is information about the dimensions of the sun porch.

Line BC is 20 feet long and runs along the living room.
Line AB is 8 feet long and is perpendicular to line BC.
Line CD is parallel to line AB but is twice as long as line AB.
Line AD represents the longest wall with the most windows.
Line AE is an imaginary line parallel to line BC.
Point E is on line CD. It is the midpoint of line CD.

How many boxes of floor tiles should Charlie order?


  1. 10 boxes
    (Jim May)

  2. 22 Boxes

  3. 22 boxes... the last 3 lines of given information (AD, AE, & E) are unnecessary.

    1. Yeah, the third- and second-to-last lines in particular are really too straightforward and should be left out of the puzzle. The last line is also a little bit too helpful as a starting hint, but after solving it, it's helpful to use that as explanation:
      The square footage of the room is the area of ABCD, which is the same as the area of ABCE added to the area of ADE. ABCE is a 20x8 rectangle and ADE is a triangle of half the size. So the area we want is ABCE+ADE=ABCE+ABCE/2=3*ABCE/2. That's 3*(20*8)/2=20*3*8/2=20*12.
      So that's 20*12 square feet, which is twenty dozen tiles. Add that to the two dozen extra and that's twenty-two dozen tiles, and since dozens of tiles are equivalent to boxes, that's 22 boxes.

  4. Mike, come back!

    1. I agree. I open up my computer every day hoping to see a new puzzle.
      Jim May

  5. Great little puzzle! I came up with 22, like the responses above.

  6. I came up with 26. the area of the rectangle portion is 20x8 plus the area of the triangle portion, 20x8/2...160+80=240, or 24 boxes, plus the 2 extra equals 26

  7. Mike, it's been a year! Come back!! :)

  8. 22 becz ABCD area 20*8+20*8/2 =12*19+(12*1/3)+(12*2/3)
    so 19+1(1/3+2/3 parts)+2 extra =22 (22 dozens tiles) or 19+2=21 (21 dozens also becz extra 2 is used for that 1/3 and 2/3 parts ) so answer is 21 or 22 it didn't mentioned whether extras can be used or not


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