How many squares and rectangles are there in a 4 by 4 grid?

Answer 1

In a 4 by 4 grid, there are 16 squares (1x1 squares), 9 rectangles that are 2x1, 6 rectangles that are 3x1, 4 rectangles that are 2x2, and 1 rectangle that is 4x4. Therefore, in total, there are 16 squares and 20 rectangles in a 4 by 4 grid.

Answer 2

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