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In a grid of A x B squares, the formula to find how many unique rectangles there are (and all squares are considered to be rectangles) is:
A * (A+1) * B * ((B+1)/4)
A and B are interchangeable.
So in a 5 x 4 grid, there are
5 * (5+1) * 4 * ((4+1)/4)
Or 5 * 6 * 4 * (5/4)
Or 150 unique rectangles.
Now if we switch A and B, the equation reads:
4 * (4+1) * 5 * ((5+1)/4)
Or 4 * 5 * 5 * (6/4)
Again 150 unique rectangles.
Wiki User
∙ 14y ago
Eliana Baker
A 4 x 5 grid has 150 rectangles because -
Formula: (n + all natural numbers before n) * (m + all natural numbers before m)
(4 + 1 + 2 + 3) * (5 + 1 + 2 + 3 + 4)
= 10 * 15
= 150
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