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

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mariloucortez's profile pic

Posted on

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.

 

justaguide's profile pic

Posted on

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's profile pic

Posted on

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`

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