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

### 3 Answers | Add Yours

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.**

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.

So,

`A = 27.53 cm^2`

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

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`

### Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes