8.5 Notes: Areas of Regular Polygons Name___________________ Objective: To find the area of a regular polygon You can circumscribe a circle about any regular polygon. The of a regular polygon is the center of the circumscribed circle. The is the distance from the center to a vertex. The is the perpendicular distance from the center to a side. Example 1: This figure is a regular pentagon with radii and an apothem drawn. Find the measure of each numbered angle. 360
Central angle =
2 1
n 3
Example 2: Find the area of a regular hexagon If we “unroll” the hexagon into the triangles to make it, it will look like this 5 in
5 in
6 in
6 in
Area of a Regular Polygon The area of a regular polygon is half the product of the apothem and the perimeter. A = A = Area a = apothem P = perimeter Example 3: Find the area of a regular decagon with a 6 in. apothem and 8 in. sides. Example 4: Some boats used for racing have bodies made of honeycomb of regular hexagonal prisms sandwiched between two layers of outer material. At the right is an end of one hexagonal cell. Find its area. 10mm
Example 5: Find the area of an equilateral triangle with a 20 in. radius. What is the area of each to the nearest square inch?