Final answer:
The total area of the small glass squares is 0 square inches because the large glass squares with a side length of 10 inches fully occupy the 40-inch side length window. No additional space is left for small glass squares.
Step-by-step explanation:
The window we are considering has side lengths of 40 inches and consists of large glass squares with side lengths of 10 inches each. To solve the problem, we'll first calculate the number of large squares that fit into the entire window. Then, we'll determine the total area of the window and subtract the area occupied by the large glass squares to find the total area of the small glass squares.
The window forms a large square with a side length of 40 inches, so its area is:
Area of window = side × side = 40 inches × 40 inches = 1600 square inches.
The area of one large glass square is:
Area of large square = side × side = 10 inches × 10 inches = 100 square inches.
To find out how many large squares fit in the window, we divide the total area of the window by the area of one large square:
Number of large squares = Total area of window / Area of one large square = 1600 / 100 = 16 large squares.
Now we'll calculate the total area occupied by the large glass squares:
Total area of large squares = Number of large squares × Area of one large square = 16 × 100 = 1600 square inches.
Since the whole window is 1600 square inches and we've calculated that 1600 square inches are occupied by large glass squares, this implies:
Total area of small glass squares = Total area of window - Total area of large squares = 1600 - 1600 = 0 square inches.
This simply means there are no small glass squares because the large squares fully occupy the window space.