Question

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

Answer 1

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.

Answer 2

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.

Answer 3

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.