To find the area of the shaded region, we need to calculate the area of the outer rectangle and subtract the area of the inner rectangle.

Step 1: Calculate the area of the outer rectangle.

The dimensions of the outer rectangle are:

• Length = 35 yards
• Width = 24 yards

The area of the outer rectangle is: $\text{Area of outer rectangle} = \text{Length} \times \text{Width} = 35 \times 24 = 840 \, \text{square yards}.$

Step 2: Calculate the area of the inner rectangle.

The dimensions of the inner rectangle are:

• Length = 27 yards
• Width = 16 yards

The area of the inner rectangle is: $\text{Area of inner rectangle} = \text{Length} \times \text{Width} = 27 \times 16 = 432 \, \text{square yards}.$

Step 3: Calculate the area of the shaded region.

The shaded area is the difference between the outer and inner rectangle areas: $\text{Shaded area} = \text{Area of outer rectangle} - \text{Area of inner rectangle} = 840 - 432 = 408 \, \text{square yards}.$

Thus, the area of the shaded region is 408 square yards.

Would you like more details or have any questions?

Related Questions:

1. How do you calculate the perimeter of the shaded region?
2. How would the shaded area change if the dimensions of the inner rectangle were increased?
3. What is the ratio of the area of the inner rectangle to the outer rectangle?
4. How can you verify the correctness of the areas calculated?
5. Can you find the length of the border between the two rectangles?

Tip:

Always double-check the units when solving area problems to ensure consistency in the final answer.