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# 10-3 Area of Polygons

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### 10-3 Area of Polygons

1. 1. Essential Understanding The area of a regular polygon is related to the distance from the center to a side Students will be able to find the area of regular polygons
2. 2. Regular Polygon A polygon with all sides and angles that are equal What are some examples of this? You can circumscribe a circle about any regular polygon. The center of the regular polygon is the center of the circumscribed circle The radius of the regular polygon is the distance from the center to a vertex. The Apothem is the perpendicular distance from the center to a side.
3. 3. Regular Polygon
4. 4. Finding Angle Measures A portion of a regular octagon has radii and an apothem drawn. What is the measure of each numbered angle?
5. 5. Finding Angle Measures A portion of a regularhexagon has radii and an apothem drawn. What is the measure of each numbered angle?
6. 6. Area of a Regular Polygon If two figures are congruent, then their areas are equal. Since each regular polygon can be divided into equal triangles, you can use the areas of those triangles to derive the area of the regular polygon The area is half the product of the apothem and the perimeter A= ½a p
7. 7. Finding Area What is the area of a regular pentagon with an 8 cm apothem and 11.6 cm sides? The side of a regular hexagon is 16 ft. What is the area of the hexagon?
8. 8. Homework Pg. 632 # 8 – 25 all 18 problems