10-3 Area of Regular Polygons

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Mathematics

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9th Grade

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Easy

Jacquelyn Duvendack

Used 3+ times

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10 Slides • 5 Questions

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.

10-3 Area of Regular Polygons

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