Answer:
There is a total of 42 squares, made up of:
- 1×1 squares = 25
- 2×2 squares = 12
- 3×3 squares = 5
Step-by-step explanation:
The given diagram shows 25 congruent small squares, each with a side length of one unit, arranged in a 1-3-5-7-5-3-1 pattern.
In a square, all four sides are of equal length, so the smaller squares can be combined to make 2×2 squares and 3×3 squares.
(Note: There are no squares bigger than 3×3 that can be made with the configuration of the pattern).
To determine the total number of squares, we can count the number of 1×1, 2×2 and 3×3 squares in each row, where the row of small squares contributes to the top edge of each larger square.
- In layer 1 there is one 1×1 square.
- In layer 2 there are three 1×1 squares, two 2×2 squares and one 3×3 square.
- In layer 3 there are five 1×1 squares, four 2×2 squares and three 3×3 squares.
- In layer 4 there are seven 1×1 squares, four 2×2 squares and one 3×3 squares.
- In layer 5 there are five 1×1 squares and two 2×2 squares.
- In layer 6 there are three 1×1 squares.
- In layer 7 there is one 1×1 square.
Adding the number of different squares together gives:
1 + 3 + 2 + 1 + 5 + 4 + 3 + 7 + 4 + 1 + 5 + 2 + 3 + 1 = 42
Therefore, there is a total of 42 squares, made up of:
- 1×1 squares = 25
- 2×2 squares = 12
- 3×3 squares = 5
