A swimming pool is in the form of a semicircular figure. Its width is 20 ft. and that parallel portions of the sides are each 20 ft. What is the are of a 5-ft-wide walk surrounding the pool? Round to the tenths.

what "sides" of a semicircle are parallel? Do you mean the circle has a diameter of 20 ft? If the base is 20 ft, then that would be the diameter of the circle.

Assuming that, we have a pool with area 1/2 pi * 10^2 = 50pi ft^2

Increase the radius by 5 ft, and you have an area of 1/2 pi * 15^2 = 225/2 pi

So, the area of the walk is 125/2 pi = 196.4 ft^2

If I have interpreted the dimensions incorrectly, fix my error and redo the calculation.

Well, to find the area of the 5-ft-wide walk around the pool, we need to first find the total area of the pool and then subtract the area of the inside portion bounded by the pool. It's like a puzzle, but with numbers!

The pool is in the form of a semicircular figure, so let's find its area. We know that the width of the pool is 20 ft, which means the radius of the semicircle is half of that, or 10 ft.

To find the area of a semicircle, we use the formula: A = (π * r^2) / 2. Plugging in the values, we get: A_pool = (π * 10^2) / 2 = 50π square feet.

Now, let's find the area of the inside portion bounded by the pool. This portion is also in the form of a semicircular figure, but with a smaller radius. The radius of the inside portion is 10 ft - 5 ft = 5 ft (as the 5-ft-wide walk surrounds the pool on all sides).

Using the same formula as before, the area of the inside portion is: A_inside = (π * 5^2) / 2 = 25π square feet.

Finally, to find the area of the 5-ft-wide walk surrounding the pool, we subtract the area of the inside portion from the area of the pool: A_walk = A_pool - A_inside = 50π - 25π = 25π square feet.

Rounding to the tenths, the area of the 5-ft-wide walk surrounding the pool is approximately 78.5 square feet.

And voilà! We've solved the puzzle and found the area of the walk around the pool.

To find the area of the 5-ft-wide walk surrounding the pool, we need to find the overall area of the larger rectangular region and subtract the area of the pool.

1. Let's start by finding the dimensions of the larger rectangular region. We know that the width of the pool is 20 ft, and there are two parallel portions of the sides each measuring 20 ft. This means that the total width of the rectangular region is 20 + 20 + 5 + 5 = 50 ft.

2. Now let's find the length of the rectangular region. Since the pool is in the form of a semicircular figure, the length is equal to the diameter of the semicircle. The diameter can be found by doubling the width, so the length is 2 * 20 = 40 ft.

3. Calculate the area of the larger rectangular region. Multiplying the length by the width gives us the area: 50 ft * 40 ft = 2000 ft².

4. Next, we need to find the area of the pool. The pool is in the form of a semicircular figure, and we can calculate its area using the formula (π * r²) / 2, where r is the radius of the pool. The radius can be found by dividing the width of the pool by 2, so the radius is 20 ft / 2 = 10 ft. Plugging this into the formula, we get (π * 10²) / 2 ≈ 157.1 ft².

5. Finally, subtract the area of the pool from the area of the larger rectangular region to find the area of the 5-ft-wide walk surrounding the pool: 2000 ft² - 157.1 ft² ≈ 1842.9 ft².

Therefore, the area of the 5-ft-wide walk surrounding the pool is approximately 1842.9 ft².

To find the area of the 5-ft-wide walk surrounding the pool, we first need to determine the radius of the pool.

Given that the width of the pool is 20 ft, we know that it is in the shape of a semicircle. The width refers to the diameter of the semicircular portion.

The formula to calculate the radius of a semicircle is:

radius = diameter / 2

In this case, the diameter is 20 ft, so:

radius = 20 ft / 2
radius = 10 ft

Now that we have the radius, we can calculate the area of the pool.

The formula to calculate the area of a circle is:

area = π * radius^2

Using π (pi) as approximately 3.14, we can plug in the values:

area = 3.14 * (10 ft)^2
area = 3.14 * 100 ft^2
area = 314 ft^2

This gives us the area of the pool.

To find the area of the 5-ft-wide walk surrounding the pool, we need to subtract the area of the pool from the area of the larger circle with a radius increased by 5 ft.

The area of the larger circle can be calculated using the formula:

area = π * (radius + width)^2

Plugging in the values:

area = 3.14 * (10 ft + 5 ft)^2
area = 3.14 * (15 ft)^2
area = 706.5 ft^2

Now, we subtract the area of the pool from the area of the larger circle:

area of walk = 706.5 ft^2 - 314 ft^2
area of walk = 392.5 ft^2

Rounding to the tenths, the area of the 5-ft-wide walk surrounding the pool is approximately 392.5 ft^2.