Regular Polygon Area
Use apothem and perimeter.
Key idea
Use apothem and perimeter.
In depth
Split a regular n-gon into n congruent triangles from the centre. Each has base s and height equal to the apothem a, so the total area is ½ × perimeter × apothem.
Worked example
A regular hexagon with side 4 and apothem 2√3 ≈ 3.46 has area ½ × 24 × 3.46 ≈ 41.6.
Formula
Real-world uses
- Calculating how much paint covers a hexagonal floor
- Estimating the area of a fountain base
Common mistake
Using the radius in place of the apothem.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Regular Polygon Area?
Use apothem and perimeter. It is a topic at the advanced level in Geometry.
What is the formula for Regular Polygon Area?
The key formula is A = ½ a P.
Where is Regular Polygon Area used in real life?
Real-world examples: Calculating how much paint covers a hexagonal floor; Estimating the area of a fountain base.
What should I learn before Regular Polygon Area?
Make sure you are comfortable with Exterior Angles of Polygons, the previous topic in Geometry.
What is a common mistake with Regular Polygon Area?
Using the radius in place of the apothem.
How can I practise Regular Polygon Area?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Regular Polygon Area?
Move on to Circles: Parts next.
Related advanced topics in Geometry
- Heron’s Formula – Triangle area from three sides.
- Arc Length of a Circle – Part of the circumference.
- Sector Area – Part of the circle’s area.
- Central and Inscribed Angles – An inscribed angle is half the central angle on the same arc.
- Chord and Tangent Properties – A tangent is perpendicular to the radius at the point of contact.
- Cones – Volume and surface area of a cone.