The formula for the area of a regular pentagon is:
Area = (1/2) * Perimeter * Apothem
Substituting the given values:
Area = (1/2) * 32cm * 3.441cm
Area = 55.088 cm^2
Therefore, the area of the regular pentagon is 55.088 cm^2.
Find the area of the regular pentagon.
Side (a): 5cm
Perimeter: 32cm
Diagonal (d): 8.09cm
Height (h): 7.694cm
Circumcircle Radius (r): 4.253
Incircle Radius (Apothem) (r): 3.441
3 answers
BZZZtt!! But thanks for playing. If you have
Side (a): 5cm
Perimeter: 32cm
then it's not a regular pentagon. Its perimeter would be 25 cm.
Side (a): 5cm
Perimeter: 32cm
then it's not a regular pentagon. Its perimeter would be 25 cm.
Oops, my mistake! Thank you for pointing that out.
Assuming the pentagon has perimeter 32cm, we can find the side length by dividing the perimeter by 5:
a = 32cm / 5 = 6.4cm
Now we can use the formula for the apothem:
Apothem (r) = a/ (2 * tan(180/5))
Apothem (r) = 6.4cm / (2 * tan(36°)) = 3.825cm
Finally, we can use the formula for the area of a regular pentagon:
Area = (1/2) * Perimeter * Apothem
Area = (1/2) * 32cm * 3.825cm = 61.2 cm^2
Therefore, the area of the regular pentagon with perimeter 32cm and side length 6.4cm is 61.2 cm^2.
Assuming the pentagon has perimeter 32cm, we can find the side length by dividing the perimeter by 5:
a = 32cm / 5 = 6.4cm
Now we can use the formula for the apothem:
Apothem (r) = a/ (2 * tan(180/5))
Apothem (r) = 6.4cm / (2 * tan(36°)) = 3.825cm
Finally, we can use the formula for the area of a regular pentagon:
Area = (1/2) * Perimeter * Apothem
Area = (1/2) * 32cm * 3.825cm = 61.2 cm^2
Therefore, the area of the regular pentagon with perimeter 32cm and side length 6.4cm is 61.2 cm^2.