1. The inside rectangle's area = y × x.
2. The the entire object's area = (y + 8) × (x + 6) = (xy + 6y + 8x + 48)
3. The shaded region's area = 6y + 8x + 48.
Step-by-step explanation:
Step 1; First we need to determine the dimensions of both the rectangles. The inner rectangle has a length of x and a width of y. The outer rectangle has a length of y + 4 + 4 = y + 8 while the width is x + 3 + 3 =x + 6.
Outer rectangle length = y + 8,
Outer rectangle width = x + 6.
Step 2; The area of a rectangle is determined by multiplying the length with the width. Area of the inner rectangle is given by;
Area of the inner rectangle = length of the inner rectangle × width of the inner rectangle. = y × x.
Step 3; Area of the outer rectangle = Length of the outer rectangle × width of the outer rectangle = (y + 8) × (x + 6) = xy + 6y + 8x + 48.
Step 4; The area of the shaded region is obtained by subtracting the area of the inner rectangle from the outer rectangle.
Shaded region's area = The outer rectangle's area - The inner rectangle's area = (xy + 6y + 8x + 48) - xy = 6y + 8x + 48.
