Find the area of the regular pentagon
Side (a): 5 cm
Perimeter: 25 in
Show work
You should get 43.01 as your answer
To find the area of a regular pentagon, we can use the formula:
Area = (1/4) * n * a^2 * cot(π/n)
Where:
- n is the number of sides (in this case, n = 5)
- a is the length of one side (in this case, a = 5 cm)
- cot is the cotangent function, which can be found on a calculator
First, we need to find the value of cot(π/5), which is the cotangent of 36 degrees (since there are 180 degrees in a pentagon, and each angle in a regular pentagon is 180(n-2)/n = 108 degrees). Using a calculator, we find that cot(36) = 1.37638192047 (rounded to 11 decimal places).
Now we can plug in the values into the formula:
Area = (1/4) * 5 * 5^2 * 1.37638192047
Area = 43.0119350147 (rounded to 11 decimal places)
Therefore, the area of the regular pentagon is approximately 43.01 square centimeters.