Areas of Polygons

You can circumscribe a circle about any regular polygon. The center of the regular polygon is the center of the circle. The distance from the center to a vertex of the regular polygon is the radius of the circle. The perpendicular distance from the center of the regular polygon to the side is called the apothem.

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GeoGebra Applet pictured above: ch10_apothem.ggb.

1. Explain how to find the area of an n-gon with apothem a and side length s.
2. If a is the length of the apothem, P is the perimeter, and A is the area of the regular polygon, find a formula relating all three of these quantities.

 

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GeoGebra Applet pictured above: ch10_polygonarea.ggb.

1. Find the area of a regular pentagon with side length 10 cm.

 

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GeoGebra Applet pictured above: ch10_trianglearea_sines.ggb.

1. Write an equation involving angle A and side lengths c and h. Solve your equation for h.
2. Find the area of the triangle in terms of angle A and side lengths b and c.