To calculate the area of a pentagon, square the length of one side (**s²**), multiply it by the constant **√[5 × (5 + 2 × √5)]**, then divide by 4. This will give you the total area of the pentagon.

## Pentagon Area Calculator

The **Pentagon Area Calculator** makes the calculation easy of both regular and irregular pentagons by using various input methods like side length, apothem, or radius. Whether you’re solving for the area of a **regular pentagon** or calculating the area of an **irregular pentagon**, this tool simplifies the process with step-by-step solutions.

The calculator can also handle different units, such as **square meters** or **square feet**, making it versatile for students, architects, and engineers. With formulas for pentagons, you can quickly find the area, whether you’re working with a **5-sided polygon** or a pentagon-based 3D shape.

**Formula:**

**$A = \frac{1}{4} \times \sqrt{5 \times (5 + 2 \times \sqrt{5})} \times s^2$**

Variable | Meaning |
---|---|

A |
Area of the pentagon |

s |
Length of one side of the pentagon |

π |
Pi (approximately 3.14159) |

**Solved Calculations :**

**Example 1:**

**Given Values**:

**s**= 6 meters

Calculation | Instructions |
---|---|

A = (1/4) × √[5 × (5 + 2 × √5)] × 6² | Square the side length. |

A = (1/4) × √[5 × (5 + 2 × 2.236)] × 36 | Calculate the square root of 5. |

A = (1/4) × √[5 × (5 + 4.472)] × 36 | Add the results inside the brackets. |

A = (1/4) × √[5 × 9.472] × 36 | Perform the multiplication inside the square root. |

A = (1/4) × √47.36 × 36 | Calculate the square root. |

A = (1/4) × 6.882 × 36 | Perform the multiplication. |

A ≈ (1/4) × 247.752 | Multiply the results by 1/4. |

A ≈ 61.94 square meters | The result gives the area of the pentagon. |

**Answer**: A ≈ 61.94 square meters

**Example 2:**

**Given Values**:

**s**= 10 centimeters

Calculation | Instructions |
---|---|

A = (1/4) × √[5 × (5 + 2 × √5)] × 10² | Square the side length. |

A = (1/4) × √[5 × (5 + 2 × 2.236)] × 100 | Calculate the square root of 5. |

A = (1/4) × √[5 × (5 + 4.472)] × 100 | Add the results inside the brackets. |

A = (1/4) × √[5 × 9.472] × 100 | Perform the multiplication inside the square root. |

A = (1/4) × √47.36 × 100 | Calculate the square root. |

A = (1/4) × 6.882 × 100 | Perform the multiplication. |

A ≈ (1/4) × 688.2 | Multiply the results by 1/4. |

A ≈ 172.05 square centimeters | The result gives the area of the pentagon. |

**Answer**: A ≈ 172.05 square centimeters

**What is Pentagon Area Calculator ?**

Calculating the area of a **pentagon** depends on whether the shape is regular or irregular. For a **regular pentagon**, the formula is **A = (1/4) × √(5(5 + 2√5)) × s²**, where **s** is the length of one side. This formula is useful when the pentagon has equal sides and angles. For an irregular pentagon, you would break it into triangles and calculate the area of each triangle before summing them up.

It makes it easy for both regular and irregular calculations, offering quick and accurate results. This tool can also be used to calculate the **area of a pentagon using the apothem**, which involves a different method: **A = 1/2 × P × a**, where **P** is the perimeter and **a** is the apothem.

Moreover, it can solve more complex problems, like determining the **surface area of a pentagonal prism** or a **pentagonal pyramid**. If you’re working with 3D shapes, the calculator provides formulas and steps to find the **surface area** or **volume**.