The numbers on a football field indicate 10 yard increments. You walk around the perimeter of a football field between the pylons. You walk a distance of 30623 yards.
Find the area and perimeter of the indicated regions. Write your answers as mixed numbers, if necessary.
a. One end zone:
Perimeter:
yd Area:
yd2
b. The playing field (not including end zones):
Perimeter:
yd Area:
yd2
c. The playing field (including end zones):
Perimeter:
yd Area:
yd2
The numbers on a football field indicate 10 yard increments. You walk around the perimeter of a football field between the pylons. You walk a distance of 30623 yards.
Find the area and perimeter of the indicated regions. Write your answers as mixed numbers, if necessary.
a. One end zone:
Perimeter:
yd Area:
yd2
b. The playing field (not including end zones):
Perimeter:
yd Area:
yd2
c. The playing field (including end zones):
Perimeter:
yd Area:
yd2
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To solve this problem, we'll need to use the information given about the distances and the dimensions of a football field.
a. One end zone:
The length of the end zone is usually about 10 yards. So, the perimeter of one end zone would be 10 + 10 + 10 + 10 = 40 yards. The area of one end zone would be the length (10 yards) multiplied by the width (53.3 yards). Therefore, the area of one end zone is 10 * 53.3 = 533 square yards.
b. The playing field (not including end zones):
The total distance you walked around the perimeter of the football field is 30623 yards. Since the distance includes both the playing field and the end zones, we need to subtract the distance of the end zones to find the distance of the playing field. Each end zone has a length of 10 yards, so the total length of both end zones is 10 + 10 = 20 yards. Therefore, the perimeter of the playing field excluding the end zones would be 30623 - 20 = 30603 yards.
To find the area of the playing field, we need to know the width of the field. Unfortunately, the width of a football field can vary, but we can assume a typical width of around 53.3 yards. So, the area of the playing field would be the length (30603) multiplied by the width (53.3). The area is 30603 * 53.3 = 1630481.9 square yards.
c. The playing field (including end zones):
To find the perimeter of the playing field including the end zones, we simply add the length of both end zones (20 yards) to the perimeter of the playing field excluding end zones (30603 yards). Therefore, the perimeter of the playing field including end zones would be 30603 + 20 = 30623 yards.
To find the area of the playing field including the end zones, we add the area of one end zone (533 square yards) to the area of the playing field excluding end zones (1630481.9 square yards). Therefore, the area of the playing field including end zones would be 1630481.9 + 533 = 1631014.9 square yards.
So, the final answers are:
a. One end zone:
Perimeter: 40 yards
Area: 533 square yards
b. The playing field (not including end zones):
Perimeter: 30603 yards
Area: 1630481.9 square yards
c. The playing field (including end zones):
Perimeter: 30623 yards
Area: 1631014.9 square yards