I agree with Puzzling's answer of 25, but I take a different approach on counting problems like this.
Each rectangle must have an upper left corner, so I look at each potential corner and count the number of rectangles for which it is the upper left corner. Then I just add them up. I think this is an easier approach, and less prone to error. It's pretty easy to get the count correct for each upper left corner. Other counting methods get tedious and I think it's easier to miss one, if you're not careful and thorough.
Answers & Comments
I agree with Puzzling's answer of 25, but I take a different approach on counting problems like this.
Each rectangle must have an upper left corner, so I look at each potential corner and count the number of rectangles for which it is the upper left corner. Then I just add them up. I think this is an easier approach, and less prone to error. It's pretty easy to get the count correct for each upper left corner. Other counting methods get tedious and I think it's easier to miss one, if you're not careful and thorough.
The number of four-sided figures which appear in the diagram:
C 25
Let me give letters to the regions:
Rectangles made out of 1 region:
a, c, d, e, f, g, h, i, j = 9 rectangles
*Note: b is not a 4-sided figure
Rectangles made out of 2 regions:
af, bd, ce, de, dg, eh, fj, gh, hi = 9 rectangles
Rectangles made out of 3 regions:
afj, ceh, ehi = 3 rectangles
Rectangles made out of 4 regions:
bcde, cehi, degh = 3 rectangles
Rectangles made out of 5 regions:
cefhi = 1 rectangle
Answer:
C) 25 rectangles