10-3 Area of Regular Polygons

10-3 Area of Regular Polygons

Multiple Choice

What does it mean to be a "regular" polygon?

• A regular polygon has all sides and angles equal.
• A regular polygon is defined by having only one angle.
• A regular polygon can have varying side lengths and angles.
• A regular polygon has unequal sides but equal angles.

Essential Understanding

The radius of a regular polygon is the distance from the center to the vertex.

The apothem is the perpendicular distance from the center to a side.

Example #1: Finding Angle Measures

Example #2: Find the measures of the angles formed by (a) two consecutive radii and (b) a radius and a side of an octagon.

Multiple Choice

What is the measure of a central angle of a regular Decagon (polygon with 10 sides)?

• 20°

• 30°

• 36°

• 45°

• 60°

Multiple Choice

What is the measure of a central angle of a regular Hexagon?

• 20°

• 30°

• 45°

• 60°

• 72°

​Postulate 10-1

If two figures are congruent, then the areas are the same.



Therefore, each triangle drawn in a regular polygon is an isosceles triangle with the same area.

Area of a Regular Polygon

Example #3: Finding the Area of a Regular Polygon

Example #4: What is the area of a regular pentagon with an 8-cm apothem and 11.6-cm sides?

Multiple Choice

The apothem of a 40-sided regular polygon is 11.4 meters. What is its area if each side measures 1.9 meters?

• 216.6 m²

• 433.2 m²

• 866.4 m²

• 1732.8 m²

Multiple Choice

Find the area of this polygon.

• 22 mm²

• 110 mm²

• 320 mm²

• 100 mm²

Example #5: Finding the Area Using Special Right Triangles!!

Remember the rules for Special Right Triangles???

Example #6: The side of a regular hexagon is 16 ft. What is the area of the hexagon? Round your answer to the nearest square foot.