The figure below represents an oval shaped track. the rounded portion of the track are semicircles. If you were to run one lap of this track, how far would you run?

Pic: LONG OVAL, THE WHOLE LENGTH IS 106 FT. THERE ARE TWO LINES NEAR THE OPPOSITE ENDS WHICH IS 12 FT LONG. (MAKES A SEMICIRCLE AT EACH END.)

To calculate how far you would run for one lap around the track, we need to consider the different segments of the track.

1. The straight segments: There are two straight segments of length 106 ft each, which make up the long sides of the oval. So, you would run a total of 2 * 106 = 212 ft for the straight segments.

2. The semicircles: There are two semicircles at each end of the oval, which are formed by the lines that are 12 ft long. To calculate the circumference of a semicircle, we use the formula C = π * r, where C is the circumference and r is the radius.

Given that the line length is 12 ft, the radius would be half of that, which is 12 / 2 = 6 ft.
So, the circumference of each semicircle is C = π * 6 = 18.85 ft.

Since there are two semicircles, the total distance covered by the semicircles would be 2 * 18.85 = 37.7 ft.

Adding the distances from the straight segments and the semicircles, you would run a total of 212 ft + 37.7 ft = 249.7 ft for one lap around this track.

To calculate the distance you would run for one lap on the oval-shaped track, you need to determine the sum of the lengths of all the segments that make up the track.

From the figure description, we can gather the following measurements:
- The total length of the oval-shaped track is 106 ft.
- There are two lines near the opposite ends, each of which is 12 ft long. These lines form semicircles at each end of the oval.

To calculate the distance run for one lap, follow these steps:

Step 1: Calculate the length of one semicircle.
The formula to calculate the circumference (C) of a circle is C = 2πr, where π is pi (approximately 3.14159) and r is the radius of the circle. Since we are given the diameter (12 ft), we can divide it by 2 to get the radius.

Radius (r) = Diameter (d) / 2
Radius (r) = 12 ft / 2
Radius (r) = 6 ft

Now, we can calculate the length of one semicircle using the formula.

Length of one semicircle (L1) = Circumference of the circle / 2
L1 = (2πr) / 2
L1 = πr
L1 = 3.14159 * 6 ft
L1 = 18.84954 ft

Step 2: Calculate the straight sections of the track.
The total length of the oval-shaped track is given as 106 ft, and the length of one semicircle (L1) is 18.84954 ft. To find the lengths of the straight sections, subtract the lengths of the semicircles from the total length.

Length of straight sections = Total length - 2(L1)
Length of straight sections = 106 ft - 2(18.84954 ft)
Length of straight sections = 106 ft - 37.69908 ft
Length of straight sections = 68.30092 ft

Step 3: Calculate the distance for one lap.
The distance for one lap is the sum of the lengths of the semicircles and the straight sections.

Distance for one lap = 2(L1) + Length of straight sections
Distance for one lap = 2(18.84954 ft) + 68.30092 ft
Distance for one lap = 37.69908 ft + 68.30092 ft
Distance for one lap = 106 ft

Therefore, for one lap of this oval-shaped track, you would run a total distance of 106 ft.

one complete circle of diameter 12

and 2 side lengths of 106