# Area of Pentagon Calculator

** Pentagon Area Calculator: **Looking for a free and handy calculator to check out the area of a pentagon? No need to search for more tools because this online Pentagon Area Calculator is the best out of all. You can easily find out the area by giving the length of the side of a pentagon in the input field of our Pentagon Area Calculator. After that, press on the calculate button to get the accurate output along with the step by step explanation.

**Here are some samples of Area of a Pentagon calculations**

Check below sections to know more information like formula, process to evaluate the pentagon area. Also, you can have a look at the some solved examples for each type of pentagon from here.

## Area of a Pentagon Formula

The most commonly used formula for evaluating the area of a pentagon is listed here.

Area of pentagon a = 1/4 ((√(5 (5 + 2 √5) s^{2})

Where, s is the length of the side of a pentagon.

The formula to calculate area of a irregular pentagon is mentioned here.

Area = width * height

height = average of y coordinates

width = difference between x coordinates

### Procedure to find Pentagon Area

If you are facing difficulty in finding the area of a pentagon you can always use our best Pentagon Area Calculator. The step by step procedure to solve the pentagon area is listed below

- Take the length of the side of a pentagon.
- The formula to compute the pentagon area is 1/4 ((√(5 (5 + 2 √5) s
^{2}) - Substitute the side length in the place of s in the above formula
- Simplify the obtained equation to get the result.

### Solved Examples

**Example 1: **Find the area of a pentagon having side 5 cm?

**Solution: **

Given that,

The length of side of a pentagon s = 5 cm

Area of pentagon = 1/4 ((√(5 (5 + 2 √5) s^{2})

Substitute the side value in the formula.

Area = 1/4 ((√(5 (5 + 2 √5) 5^{2})

= 1/4 ((√(5 (5 + 2 √5) * 25)

= 43.01

∴ Area of Pentagon side 5 cm is 43.011935 cm^{2}

**Example 2: **Use the area of an irregular polygon method to find the area of the pentagon with coordinates (2, 2), (5, 7), (8, 3), (9, 0) and (6, 1)?

**Solution: **

Given that,

The vertices of a polygon are A(2, 2), B(5, 7), C(8, 3), D(9, 0) and E(6, 1)

Let us take AB, BC, CD, DE, EA are the sides of a pentagon.

x1 | y1 | x2 | y2 | Ht | W | A |
---|---|---|---|---|---|---|

2 | 2 | 5 | 7 | 4.5 | 3 | 13.5 |

5 | 7 | 8 | 3 | 5 | 3 | 15 |

8 | 3 | 9 | 0 | 1.5 | 1 | 1.5 |

9 | 0 | 6 | 1 | 0.5 | -3 | -1.5 |

6 | 1 | 2 | 2 | 1.5 | -4 | -6 |

Total: | 22.5 |

∴ Area of Pentagon side is 22.5 sq units.

Check out all our handy calculator tools on area, volume, perimeter, surface area, etc of geometric shapes from Areavolumecalculator.com to improve your skills and understand the concepts easily.

### FAQs on Pentagon Area Calculator

**1. How do you find area of a pentagon?**

The simple way to calculate the area of a pentagon is place the side value in the pentagon area formula and do further simplification to get the result.

**2. How many sides does a pentagon has?**

Pentagon has 5 sides and 5 vertices. A regular pentagon is nothing but a geometrical shape of 5 sides and all sides are in equal length.

**3. How do you find the length of a side of a pentagon when the area is given?**

As we know that area a = 1/4 ((√(5 (5 + 2 √5) s^{2})

(4 * a) / (√(5 (5 + 2 √5) ) = s^{2}

side = √[(4 * a) / (√(5 (5 + 2 √5) )]

**4. Where can I get the detailed process to calculate the area of an irregular pentagon?**

You can check this page to get the formula to find area of an irregular pentagon with help of solved example.