To solve this problem, let's find the area of the track around the swimming pool.

Step 1: Determine the area of the larger rectangle (the outer dimensions, including the track)

The outer dimensions include the swimming pool plus the 10 m wide track on each side. Thus:

• Outer Length = $50 \, \text{m} + 10 \, \text{m} + 10 \, \text{m} = 70 \, \text{m}$
• Outer Width = $25 \, \text{m} + 10 \, \text{m} + 10 \, \text{m} = 45 \, \text{m}$

Now, we calculate the area of the outer rectangle: $\text{Area of Outer Rectangle} = 70 \, \text{m} \times 45 \, \text{m} = 3150 \, \text{m}^2$

Step 2: Determine the area of the inner rectangle (the swimming pool itself)

The swimming pool has dimensions:

• Inner Length = 50 m
• Inner Width = 25 m

The area of the inner rectangle (the swimming pool) is: $\text{Area of Inner Rectangle} = 50 \, \text{m} \times 25 \, \text{m} = 1250 \, \text{m}^2$

Step 3: Calculate the area of the track

The area of the track is the difference between the area of the outer rectangle and the inner rectangle: $\text{Area of Track} = \text{Area of Outer Rectangle} - \text{Area of Inner Rectangle} = 3150 \, \text{m}^2 - 1250 \, \text{m}^2 = 1900 \, \text{m}^2$

Answer

The area of the track around the swimming pool is: $\boxed{1900 \, \text{m}^2}$

Would you like more details or have any questions?

Related Questions

1. What would be the area of the track if its width were changed to 5 m?
2. How would the area change if the swimming pool was a square with the same outer dimensions?
3. What is the perimeter of the outer rectangle (including the track)?
4. How can we calculate the area of a circular track if the swimming pool were circular?
5. If the width of the track increased by 2 m on each side, how would the area of the track change?

Tip

To find the area of a track or border around a shape, calculate the areas of the outer and inner shapes separately, then find the difference.