Unit 10 · Measurement and Three-Dimensional Geometry

10.3Area of Regular Polygons

Quick Answer

Area of a regular polygon: A = ½aP, where a is the apothem (perpendicular distance from center to a side) and P is the perimeter. This formula comes from dividing the polygon into congruent triangles.

Essential Question

How does the apothem of a regular polygon serve the same role as the height in the triangle area formula?

Learning Goals

  • 1Define apothem and identify it in a regular polygon.
  • 2Apply the formula A = ½aP to find the area of a regular polygon.
  • 3Use special right triangles to find the apothem.
  • 4Find the area of regular hexagons, squares, and other regular polygons.

Key Vocabulary

Apothem

The perpendicular distance from the center of a regular polygon to one of its sides.

Regular polygon area formula

A = ½aP, where a is the apothem and P is the perimeter.

Center of a regular polygon

The point equidistant from all vertices of a regular polygon.

Full lesson content coming soon

Worked examples, guided practice problems, a workbook, quiz, and downloadable PDF resources will be added to this lesson in Phase 2. The learning goals and vocabulary above reflect the complete lesson scope.