A fish pond at the local park is a regular hexagon.
a. Write a formula for the perimeter of the pond in terms of the length of a side. Explain your formula.
b. Each side has a length of 7.5 feet. Find the perimeter of the pond.
c. Suppose the designer of the pond wants to make another regular hexagonal pond with a perimeter of 57.6 feet. Find the length of one side of the pond. Explain your method.
a. P = 6s
b.
P = 6 * 7.5
P = ?
whats c?
C is 0. Zero being the grade you will get once your teacher realizes you CHEATED!
a. The formula for the perimeter of a regular hexagon can be derived by recognizing that a regular hexagon is made up of six equilateral triangles. Each side of a hexagon is equal in length, and since all three sides of an equilateral triangle are equal, the perimeter of a hexagon is six times the length of one of its sides. Therefore, the formula for the perimeter of a regular hexagon in terms of the length of a side, denoted as "s", is P = 6s.
b. Given that each side has a length of 7.5 feet, we can use the formula P = 6s, where s = 7.5, to find the perimeter of the pond. Substituting the value of s into the formula, we get P = 6 * 7.5 = 45 feet. Therefore, the perimeter of the pond is 45 feet.
c. To find the length of one side of a pond with a perimeter of 57.6 feet, we can rearrange the formula P = 6s to solve for s. Dividing both sides of the equation by 6, we get s = P/6. Substituting the given perimeter, P = 57.6, into the formula, we find s = 57.6/6 = 9.6 feet. Therefore, the length of one side of the pond is 9.6 feet.