10.5 Area of Regular Polygons

1. 10.5 Area of Regular Polygons

2. Vocabulary Areas of Regular Polygons What You'll Learn You will learn to find the areas of regular polygons. 1) center 2) apothem

3. Areas of Regular Polygons Every regular polygon has a ______, center a point in the interior that is equidistant from all the vertices. A segment drawn from the center that is perpendicular to a side of the regular polygon is called an ________. apothem congruent In any regular polygon, all apothems are _________.

4. a s Areas of Regular Polygons Now, create a triangle by drawing segments from the center to each vertex on either side of the apothem. Now multiply this times the number of triangles that make up the regularpolygon. The figure below shows a center and all vertices of a regular pentagon. The area of a triangle is calculated with the following formula: perpendicular An apothem is drawn from the center, and is _____________ to a side. There are 5 vertices and each is 72° from the other (360 ÷ 5 = ___.) 72 72° 72° 72° 72° 72° What measure does 5s represent? perimeter Rewrite the formula for the area of a pentagon using P for perimeter.

5. Areas of Regular Polygons P

6. 8 ft 5.5 ft Areas of Regular Polygons Find the area of the shaded region in the regular polygon. Area of polygon Area of triangle triangle To find the area of the shaded region, subtract the area of the _______ from the area of the ________: pentagon The area of the shaded region: 88 ft2 110 ft2 – 22 ft2 =

7. 6.9 m 8 m Areas of Regular Polygons Find the area of the shaded region in the regular polygon. Area of polygon Area of triangle triangle To find the area of the shaded region, subtract the area of the _______ from the area of the ________: hexagon The area of the shaded region: 110.4 m2 165.6 m2 – 55.2 m2 =

8. Areas of Regular Polygons End of Lesson