Find the area and perimeter of a regular (equal-sided) pentagon from its side length alone.
How it works
Perimeter is simply five times the side length. Area uses the regular-polygon formula Area = ¼ × √(5 × (5 + 2√5)) × side² — a side length of 10 gives an area of about 172.05 and a perimeter of 50.
What this does not include
This is for a regular pentagon only, where all five sides and angles are equal. An irregular pentagon needs a different method — typically breaking it into triangles — not covered here.
How to use this calculator
- Enter the side length.
A worked example
A regular pentagon with side 10: area = 172.0477, perimeter = 5 × 10 = 50.
Side 4: area = 27.5276, perimeter = 20.
What the variables mean
| Variable | Meaning |
|---|---|
| Side length | Length of each of the pentagon’s five equal sides |
Edge cases worth knowing
This assumes a regular pentagon — five equal sides and angles. An irregular pentagon (like an actual home plate shape) needs individual side and angle data this single input can’t capture.
Area scales with the square of the side length — the 2.5× jump in side length above (4 to 10) produces about a 6.25× jump in area, matching 2.5².
What’s the interior angle of a regular pentagon?
Each interior angle measures 108°, found from the general regular-polygon formula (n − 2) × 180° ÷ n with n = 5.
Why is the area formula so much more complex than the perimeter formula?
Area depends on the pentagon’s height as well as its side length, and that height involves the golden ratio through the √5 term — a mathematical relationship unique to the pentagon among common polygons.
Does this work for a pentagon drawn any orientation?
Yes — area and perimeter don’t depend on how the shape is rotated, only on its side length.
