Keep on counting
Find the total number of rectangles (with squares included) in a
square grid.
Extra: Find a general expression for grid
The answer is 540.
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1 solution
Consider a coordinate system with origin at one corner of gird and x axis along the longer side of grid.
Let the coordinates of rectangle be (a,b) , (a,c) , (d,b) and (d,c). where 0 < = a < d < = 8 and 0 < = b < c < = 5
There are 9C2 possible combinations of a and d. And 6C2 combinations of b and c.
Therefore, by the rule of product there are 9C2 x 6C2 = 540 combinations of a,b,c and d. And thus 540 different rectangles.