Area of Regular Polygons Regular – congruent sides and angles

Find the area of this regular pentagon, you know the Perimeter is 200 inches.

Area 1.Divide the polygon into Triangles – one vertex is the center of the polygon and the side of the polygon is the base of the triangle – this form congruent isosceles triangles 2.Find the central angle of each of the triangles – angle formed at the center 3.Calculate the altitude of the triangle using trig ratios 4.Find the area of the triangle 5.Find the area of the polygon by multiplying by how many triangles there are

Apothem Apothem is the perpendicular distance from the center of the polygon to one side (height of the triangle) If you know the apothem you can find the area as well a=apothem s=side lengths n=number of sides

Examples

Circles Exact answer or in terms of pi – do not multiply out the pi value Approximate value is when you use, 3.14, 22/7 or the pi button on calculator

Examples

Homework All Due 4/21 Pg , 7 and 8 Find Area given Regular Octagon with perimeter 1600 in Find area given Regular Decagon with perimeter 1200 cm Pg odd Honors 12 and 13