Pentagon Area

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Pentagon Area Calculation:

  •  a =

    Length of a single side

  •  A =

    Area of the pentagon

  •

    Choose the number of decimals to show in your answer. This is also known as significant figures. Select an appropriate amount of significant figures based on the precision of the input numbers.

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Pentagon Area Formula

Given the side length of a pentagon the area can be calculated using the formula below.

A = 1/4 * √(5 * (5 + 2 * √5)) * a2

Pentagon Area Variables

A pentagon is a two-dimensional shape with five even sides. The length of one side can be used to find the area.

Side (a)
Length of one side of the pentagon in linear units.
Area (A)
Area of a pentagon in square units.

Pentagon Area Solution

What is the area of a pentagon given the side length of 5?

  • A = 1/4 * √(5 * (5 + 2 * √5)) * a2
  • Substitute in the known values
  • A = 1/4 * √(5 * (5 + 2 * √5)) * 52
  • Find the area given a side length (a) of 5
  • A = 1/4 * √(5 * (5 + 2 * 2.236)) * 52
  • Start solving on the interior bracket, square root first, rounding to three decimals
  • A = 1/4 * √(5 * (5 + 4.472)) * 52
  • Continue solving the interior bracket with multiplication next
  • A = 1/4 * √(5 * (9.472)) * 52
  • Completely solve the interior bracket
  • A = 1/4 * √(47.36) * 52
  • Solve the next bracket under the square root
  • A = 1/4 * 6.882 * 25
  • With brackets gone calculate the root and power, rounding to three decimals
  • A = 43.0125
  • Complete the solution with multiplication
  • 43.0125

A pentagon with a side of 5 units will have an area of about 43.0125 square units.

Pentagon Area Example

If a pentagon has a side of 15 cm what is the area?

  • A = 1/4 * √(5 * (5 + 2 * √5)) * a2
  • A = 1/4 * √(5 * (5 + 2 * √5)) * 152
  • A = 1/4 * √(5 * (5 + 2 * 2.236)) * 152
  • A = 1/4 * √(5 * (5 + 4.472)) * 152
  • A = 1/4 * √(5 * (9.472)) * 152
  • A = 1/4 * √(47.36) * 152
  • A = 1/4 * 6.882 * 225
  • ~387.1125 cm2

A pentagon with a side length of 15 cm has an area of about 387.1125 cm2.

Want to convert area measurements?

Area Unit Converters