441
Oh, dude, you're really making me count rectangles now? Ok, fine. So, in a 5 by 4 grid, you've got 15 horizontal lines and 10 vertical lines, which means you've got 15 x 10 = 150 rectangles. But hey, who's counting, right?
Oh, that's a happy little question! In a 6x6 grid, you have 36 individual squares. But if you count all the different sizes of squares that can fit within the grid, including the whole grid itself, you have a total of 91 squares to enjoy painting with your imagination.
30
Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. So, there are 5 rectangles with an area of 36 cm^2 is 5.
1 x 42 2 x 21 3 x 14 6 x 7
126 rectangles. 1 Strip of 6 equals 21 rectangles, multiply by 1 strip of 3 which makes 6, is 126 rectangles, all in one big rectangle.
Oh, dude, let me count... Okay, so in a 5 by 6 grid, you've got like 15 horizontal rectangles and 10 vertical rectangles, but don't forget the big one that covers the whole grid, so that's like 26 rectangles total. So, like, yeah, there you go.
36
In a 3x3 grid, you can form rectangles by choosing two horizontal and two vertical lines. A 3x3 grid has 4 horizontal lines and 4 vertical lines. The number of ways to choose 2 lines from 4 is given by the combination formula ( C(4, 2) ), which equals 6. Therefore, the total number of rectangles is ( 6 \times 6 = 36 ).
16 1x1 rectangles + 12 2x1 rectangles + 8 3x1 rectangles + 4 4x1 rectangles + 12 1x2 rectangles + 9 2x2 rectangles + 6 3x2 rectangles + 3 4x2 rectangles + 8 1x3 rectangles + 6 2x3 rectangles + 4 3x3 rectangles + 2 4x3 rectangles + 4 1x4 rectangles + 3 2x4 rectangles + 2 3x4 rectangles + 1 4x4 rectangle. A Grand Total of: 100 squares and rectangles. OR: A rectangle is formed by 2 horizontal lines and 2 vertical lines. There are 5 horizontal and 5 vertical lines so the number of rectangles is 5C2 * 5C2 = 10 * 10 = 100
Well, honey, in a 3 by 4 grid, there are 36 rectangles. That's right, I said 36. You got your 12 1x1 squares, 6 2x1 rectangles, 6 1x2 rectangles, 4 2x2 squares, and 4 3x2 rectangles. So, there you have it, 36 rectangles in total.
A number is a "square number" if it corresponds to a square arrangement of dots in a regular grid pattern. The first few square numbers are...1:.4: (2 x 2 grid). .. .9: (3 x 3 grid). . .. . .. . .and so on.36 is a square number because that's how many dots are in a 6 x 6 grid.. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .
There are 36 unique quadrilaterals in a 3x3 square grid: 14 squares = 9 (1x1) 4 (2x2) 1 (3x3) 22 rectangles = 6 (1x2) 6 (2x1) 6 (3x3) 2 (2x3) 2 (3x2) (the total number of quadrilaterals formed by 3 x 3 pin sets will be larger, i.e. 78)
Well, honey, in a 4 x 6 grid, you've got a total of 30 rectangles. You've got your 24 smaller rectangles formed by the individual squares, then you add 4 rectangles formed by 2 x 2 squares, and finally, you top it off with 2 rectangles formed by 3 x 2 squares. So, grab a calculator if you need to, but that's the tea!
Oh, dude, you're really making me count rectangles now? Ok, fine. So, in a 5 by 4 grid, you've got 15 horizontal lines and 10 vertical lines, which means you've got 15 x 10 = 150 rectangles. But hey, who's counting, right?
6
5