Landscaping a patio with DIAGONALLY placed tile and turf "groutlines"

Question

1.  how many 2'x2' tiles and .5' turf sections will I need to complete a patio that is 76'x24' ?  

 

Extra information:

 There will be an area in the center 12'x10' that doesn't need any tile or turf.

Answer 1

     Let's take a simpler problem first. a 24' by 76' room, no grout, no center area missing using 2' by 2' tiles. We need to determine how many diagonals of the tiles fit inside this room. Using the pythagorean theorem, the diagonal is 2sqrt 2....approx 2.828 ft. so 76/2.828 = 26.87 diagonals by 24/2.828 = 8.49 diagonals. So far, in terms of full tiles we've got 26 *8 = 208 of these tiles. Now comes pieces of tiles, some to finish the rows and columns but much more to fill up the little triangles that are missing all along the border. You will now have to cut a tile taking off .13 of a diagonal leaving yourself a big piece of tile shaped like home plate having .87 of a diagonal. You will have to do this 8 times to complete the 8 rows.....Doing a similar thing in the other direction, you would cut off .51 of a diagonal to leave yourself .49 pieces and you'll need 26 of them....so there is another 26 tiles. So we're at 208+8+26=242 tiles. We still have a weird piece in that one corner makes 243 tiles. Note, you could have just said 27*9. We still have those little triangles along the edges. The triangles along 2 of the edges are just 1/2 tiles and I have 26 scrap cut off pieces of .51 so I can use those to fill in the 26 edge triangles along one side so I dont need to cut whole tiles.  The other scraps are too small to do anything with. So we have 3 more edges to do. You need 4 more tiles to cut into halves to place along the other nice edge. So we're up to 251 tiles. So we have 26 triangles and 8 triangles and 4 corners left. I'm tired of typing and this is incredibly hard to describe without a diagram so I'll tell you what most people do. If you take 1 tile and cut it twice along both diagonals, 3 out of the 4 fit perfectly into the corners. So we've got 252 tiles. Most people just use one tile and cut off opposite coners to fill in the remaining 34 triangles, so you'll need 17 more tilesbringing us up to 269. We are still missing one corner that you'll have to cut from a full tile bringing us to 270. Sometimes, the edge triangles are small enough to use a full tile and cut off all 4 corners rather than just the opposite corners. Without a diagram, this is impossible.

AND THIS IS THE EASY VERSION!!!!! You can see why people don't tile on the diagonal often. I've done it twice, once with grout and once without.

    I hope this helps you in some way.....you can also appreciate why other tutors didn't respond.

Good luck with your problem.

 If I could speak with you, it would be so much easier.

You're absolutely right....I forgot 25x8 tiles. Imagine a row of 26 diagonal laid tiles. If you put another 26 tiles under them, matching up points, you would have 25 squares formed by them and then one extra that would fit against the cut off tiles making 26.

     So, one thing you're forgetting is that the area of the tiles is each 4 sq feet so 470x4 = 1880 and we needed 24x76=1824.....only 56 sq feet lost to cutting and scrapping. This sound close because I only cut and scrapped on the 17 edge tiles and the one corner.