Answer:
To find the total area of rectangle ABCD, we need to calculate the sum of the areas of all the squares and rectangles within it.
1. Let's start by calculating the area of each square labeled "L". Since each large square has sides measuring x inches, the area of one large square is x * x = x^2 square inches. Since there are 2 large squares, the total area contributed by the large squares is 2 * x^2 = 2x^2 square inches.
2. Next, let's calculate the area of each small square labeled "s". Each small square has sides measuring y inches, so the area of one small square is y * y = y^2 square inches. Since there are 15 small squares, the total area contributed by the small squares is 15 * y^2 = 15y^2 square inches.
3. Finally, let's calculate the area of each rectangle labeled "R". Each rectangle has sides measuring x inches and y inches, so the area of one rectangle is x * y = xy square inches. Since there are 13 rectangles, the total area contributed by the rectangles is 13 * xy = 13xy square inches.
To find the total area of rectangle ABCD, we add up the areas of the large squares, small squares, and rectangles:
Total area = 2x^2 + 15y^2 + 13xy square inches.
Therefore, the total area of rectangle ABCD is 2x^2 + 15y^2 + 13xy square inches.
Explanation: