Pentagon Area Calculator – Guide & Formulas
Calculate the area, perimeter, and apothem of a regular pentagon using side lengths or circumradius.
Find the area, perimeter, apothem, and diagonal lengths of a regular five-sided pentagon from a single known input.
Key Takeaway
Use the free Pentagon Area Calculator to calculate the area, perimeter, and apothem of a regular pentagon using side lengths or circumradius. Get instant results with step-by-step explanations.
How to Use the Pentagon Area Calculator
- Enter the side length of the regular pentagon.
- Review the calculated area, perimeter, and inner apothem (radius of inscribed circle).
- Analyze the geometric steps based on dividing the pentagon into 5 congruent triangles.
The Formula
Variable Definitions
- s: Side length of the regular pentagon
- A: Total calculated surface area
Footprint of a Pentagon Sandbox
Find the floor area of a pentagonal sandbox with sides measuring 6 feet.
- Step 1: Set side length s = 6 feet.
- Step 2: Square the side length: 6² = 36.
- Step 3: Apply the multiplier: 1.72048 * 36 ≈ 61.94 square feet.
- Step 4: The sandbox footprint is approximately 61.94 square feet.
Frequently Asked Questions
What is the sum of angles in a pentagon?
The interior angles of any pentagon always sum to 540 degrees. For a regular pentagon, each interior angle measures exactly 108 degrees.
What is the apothem of a pentagon?
The apothem is the distance from the pentagon's center perpendicular to the midpoint of any side, calculated as s / (2 * tan(36°)).
How many diagonals does a pentagon have?
A pentagon has exactly 5 diagonals, which form the classic star pentagram outline.