10 3 Areas of Regular Polygons Essential Understanding

10 -3 Areas of Regular Polygons

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

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.

Regular Polygon

Finding Angle Measures A portion of a regular octagon has radii and an apothem drawn. What is the measure of each numbered angle?

Finding Angle Measures A portion of a regular octagon has radii and an apothem drawn. What is the measure of each numbered angle?

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=½ap

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?

Homework Pg. 632 # 8 – 25 all 18 problems