How many squares of all sizes are in a 6x6 grid of squares?
2006-12-15 14:18:20 · 13 answers · asked by Sally 2 in Science & Mathematics ➔ Mathematics
The common factors of 6 are 1, 2, 3, and 6
Since a square is equilateral, the squares must be 1x1, 2x2, 3x3, and 6x6
You may try drawing this out on graph paper, or do it logically, but the answers will turn out the same, whatever works for you:
A 6x6 grid of squares has 36 squares, so...
36 squares / 1x1 square
36/1 = 36 squares
36 squares / 2x2 square
36/4 = 9 squares
36 squares / 3x3 square
36/9 = 4 squares
36 squares / 6x6 square
36/36 = 1 square
Add all of them together:
36 + 9 + 4 + 1 = 50
2006-12-15 15:12:36 · answer #1 · answered by Anonymous · 0⤊ 6⤋
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in a 6 x 6 grid the total number of squares is 92 from 1 (6x6) + 4 (5x5) + 10 (4x4) + 16 (3x3) + 25 (2x2) + 36 (1x1) squares.
2016-04-04 21:55:38 · answer #2 · answered by Anonymous · 0⤊ 1⤋
How many 6x6 squares: 1
How many 5x5 squares: 4
How many 4x4 squares: 9
A pattern develops...
3x3: 16
2x2: 25
1x1: 36 (as a check, this is right)
So the answer is 91
2006-12-15 14:26:32 · answer #3 · answered by sofarsogood 5 · 2⤊ 0⤋
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How many squares of all sizes are in a 6x6 grid of squares?
How many squares of all sizes are in a 6x6 grid of squares?
2015-08-16 15:03:53 · answer #4 · answered by Anonymous · 0⤊ 0⤋
6^2+5^2+4^2+3^2+2^2+1^2 = 36+25+16+9+4+1 = 36+25+30 = 66+25 = 91
91 squares in total including the big one. gee, sounds like an average mormon tabernacle!
2006-12-15 14:58:39 · answer #5 · answered by Anonymous · 0⤊ 0⤋
Take each possible square size and figure out the # of possible positions, then add them up:
1x1 squares: 6x6 = 36
2x2 squares: 5x5 = 25
3x3 squares: 4x4 = 16
4x4 squares: 3x3 = 9
5x5 squares: 2x2 = 4
6x6 squares: 1x1 = 1
Total: 91
2006-12-15 14:26:58 · answer #6 · answered by John's Secret Identity™ 6 · 4⤊ 0⤋
SPOILER: I didn't include the answer, but only how to get it. But the answer is more than 50.
Draw the 6x6 grid. For each square, count how many squares in the grid have that square as its upper-left corner. For example, in the following grid of Os:
OOOOOO
OOOOOO
OOOOOO
OOOMOO
OOOOOO
OOOONO
There are 3 squares that have M in the upper-left corner, and 1 square with N in the upper-left corner. Now do this for all squares, and add them up.
Extra credit: If you want to generalize this to the n-by-n grid case, you'll probably want to count the squares in a more clever way.
2006-12-15 14:29:12 · answer #7 · answered by larry 1 · 0⤊ 0⤋
7
2006-12-15 14:24:59 · answer #8 · answered by friend 1 · 0⤊ 1⤋
6x6 Grid
2016-11-14 04:16:27 · answer #9 · answered by staton 4 · 0⤊ 0⤋
36
2006-12-16 02:31:26 · answer #10 · answered by Michael 2 · 0⤊ 2⤋