Find the area of a regular pentagon with a side length of 4 cm.

Expert Answers
mariloucortez eNotes educator| Certified Educator

To find the area of any regular polygon given the length of the sides, use the formula:

`A = (n/4)*s^2 * cot(pi/n)`

``where n is the number of sides

          s is the length of the sides

Identify the given of the problem:

s = 4

n = 5 since it is a pentagon

Applying the formula, you have:

`A = (5/4)*4^2* cot(pi/5)`

If you input `pi`  , be sure that your calculator is in degree mode. If it is in degree mode, you can convert into degrees.`pi = 180 degrees` . 

cot function is the inverse of tan. To have cot, input `1/(tan(pi/5))`  in your calculator. 



`A = 27.53 cm^2`

Answer rounded in 2 decimal places. Don't forget to place the unit.


justaguide eNotes educator| Certified Educator

The area of a regular polygon with n sides of length s is A = `(1/4)*n*s^2*cot(180/n)`

For a regular pentagon with sides 4 cm, n = 5, s = 4. The area is `(1/4)*5*4^2*cot(180/5)` = 27.527

The area of the regular pentagon is 27.527 square cm.

oldnick | Student

Area pentagon is equivaletne at  sum five triangles  with bases the side  and height the. apoteme.

`S= 5/2( l xx l xx 0.688= 27.52 cm^2`