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3. Geometry
4. Pentagon Area

\(s\)

(length of side)

units

Area

square units

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How to use Pentagon Area Calculator

1. Enter ✎ value for length of side \((s)\).
2. The result appears beneath the inputs as you enter values.

About this calculation

The area of a regular pentagon is a measure of the space enclosed by its five equal sides. To calculate the area of a pentagon using length of the side, use the given formula for pentagon area, and compute the result.

Formula

To calculate the pentagon area, you can use the following formula.

Area = \( \frac{ \sqrt{5(5 + 2\sqrt{5})} }{4} s ^2 \)

where

Calculation

{
  "topic": "pentagon-area",
  "img": {
    "width": 245,
    "height": 273
  },
  "input_types": [
    "float"
  ],
  "input_labels": [
    "s"
  ],
  "input_values": [
    "8"
  ],
  "input_units": [
    "units"
  ],
  "input_descriptions": [
    "length of side"
  ],
  "examples": [
    {
      "s": 20
    },
    {
      "s": 1
    }
  ],
  "type": "Calculate",
  "title": "Pentagon Area",
  "category": "Geometry",
  "shape": "Pentagon",
  "formula_mathjax": "\\( \\frac{ \\sqrt{5(5 + 2\\sqrt{5})} }{4} s ^2 \\)",
  "formula_mathjax_sub": "\\( \\frac{ \\sqrt{5(5 + 2\\sqrt{5})} }{4} \\times s ^2 \\)",
  "formula": "( Math.sqrt(5*(5+2*Math.sqrt(5))) * s * s / 4 )",
  "op_label": "Area",
  "output_unit": "square units",
  "description": "The Pentagon Area calculator calculates the area of a pentagon shape by taking the length of its side as input.",
  "explanation": "The area of a regular pentagon is a measure of the space enclosed by its five equal sides. To calculate the area of a pentagon using length of the side, use the given formula for pentagon area, and compute the result."
}