Area of Regular Polygon

A regular polygon can be split into equal triangles by drawing lines from its center to each vertex. Each triangle has the same height, which is the apothem, and all of the triangle bases add up to the full perimeter, so the total area is half of apothem times perimeter. This is why the formula matches the familiar triangle area idea: area = 1/2 × base × height, applied to the whole polygon at once.

Use this formula when you know the apothem and perimeter of a regular polygon, such as a regular hexagon, octagon, or dodecagon. It is especially useful in geometry problems, design work, tiling, and engineering calculations involving symmetric shapes.

• Using the side length instead of the full perimeter
• Confusing the apothem with the slant height or the side length
• Forgetting to square the units in the final area answer