A pentagon with the a perimeter of 45 feet , what is the area
if it is a regular pentagon then each side is 9 feet.
We could draw 5 identical isosceles triangles with sides 9 and contained angle of 360/5° or 72°
Area of one of these = (1/2)(9)(9)sin72 = 38.517789
but we have 5 of them so
total area = 192.59 ft^2
To find the area of a regular pentagon, we need to know either the apothem or the side length. If we have the side length, we can use the formula:
Area = (1/4) * √(5(5 + 2√5)) * s²
Given the perimeter of the pentagon is 45 feet, we can find the side length by dividing the perimeter by 5:
Side length = Perimeter / 5 = 45 / 5 = 9 feet
Now, we can calculate the area of the pentagon using the formula:
Area = (1/4) * √(5(5 + 2√5)) * (9)^2
Area = (1/4) * √(5(5 + 2√5)) * 81
Area ≈ 194.92 square feet
Therefore, the area of the pentagon is approximately 194.92 square feet.
To find the area of a pentagon, you need either the length of its apothem (distance from the center of the pentagon to a side) or the length of one of its sides. However, in this case, we are only given the perimeter of the pentagon, not the length of any particular side or the apothem.
Since we don't have enough information to directly calculate the area, we can provide some possible scenarios based on different assumptions:
1. Regular Pentagons: If we assume the pentagon to be regular, meaning all sides and angles are equal, we can calculate the length of each side by dividing the perimeter by 5 (since a pentagon has 5 sides). In this case, each side would be 9 feet (45 feet divided by 5). However, without the apothem length, we still cannot calculate the exact area.
2. Non-Regular Pentagons: If we assume the pentagon to be irregular, with different side lengths, it becomes even more difficult to directly calculate the area without additional information like angles or side lengths.
Therefore, without more information, it is not possible to determine the exact area of the pentagon with just the given perimeter of 45 feet.