Four congruent square corners are cut off from the large square of cardboard.
Find three expression in terms of x and y to calculate shaded area.
what is 2-2
no idea what is shaded, nor what x and y represent.
But two possibilities are (x-2y)^2 and 4y^2
To find the shaded area, we need to consider the area of the large square minus the areas of the four congruent square corners.
Let's denote the side length of the large square as 'L'. Since the large square was formed by cutting off four congruent square corners, the side length of each cut-off corner square is 'x'.
1. Expression for the area of the large square:
The area of a square is calculated by squaring its side length. Therefore, the area of the large square is L^2.
2. Expression for the area of one cut-off corner square:
The area of a square is calculated by squaring its side length. Therefore, the area of one cut-off corner square is x^2.
3. Expression for the total area of the four cut-off corner squares:
Since there are four identical corner squares, the total area of the four cut-off corner squares is 4 times the area of one cut-off corner square, which is 4x^2.
To find the shaded area, we subtract the total area of the four cut-off corner squares from the area of the large square:
Shaded Area = Area of the large square - Total area of the four cut-off corner squares
Shaded Area = L^2 - 4x^2
Therefore, three expressions in terms of x and y to calculate the shaded area are:
1. Shaded Area = L^2 - 4x^2
2. Shaded Area = y^2 - 4x^2
3. Shaded Area = (y - 2x)^2