Compute area from a regular polygon's side count and common side length. Its area sits beside the working formula for a quick arithmetic check.
The roles assigned to number of sides and side length explain the operation that produces area.
For a regular hexagon with side 5, area is 6 × 5² ÷ (4 tan(π/6)), approximately 64.9519 square units. The familiar hexagon formula 3√3s²/2 is equivalent. This Regular Polygon Area example can be compared with other shape areas.
Convert the central angle to π/n inside the tangent, square the side length, multiply by the side count, and divide by four times the tangent. Keep the calculator in radian mode for π/n.
The side count must be a whole number and the figure must be regular. Irregular polygons with the same side count and side length can have different areas.
The formula supports symmetric paving pieces, signs, table tops, frames, and geometric models when a common side measurement is easier to obtain than an apothem.
Side length alone determines area only because regularity fixes every angle. An irregular polygon needs additional dimensions, coordinates, diagonals, or a decomposition into simpler shapes. Here the requested quantity is specifically area.
A regular polygon has equal sides and equal angles. Joining its center to every vertex creates congruent isosceles triangles whose combined area can be expressed with n, side length s, and tan(π/n). For a connected concept in Regular Polygon Area, see interior angles.
Preserve Number of sides when checking the Regular Polygon Area output. Keep Side length under the same convention and estimate Area. A controlled change to Side length should move the Regular Polygon Area Area in a mathematically consistent direction.
Square units based on the entered side unit, such as square centimeters.
No. A polygon has a whole number of sides.
Yes. With n = 4 it simplifies to side squared.
It is the perpendicular distance from a regular polygon's center to a side.