Areas of Regular Polygons 10-3

Honor’s On a sheet of warm up paper: Write the name of your podcast group members (don’t write your own name) Rate each member from 1-10, 10 being “very helpful”

Area Formulas Rhombus:.5(D1)(D2) Trapezoid:.5(h)(b1+b2) Kite: There ain’t one, use your common sense!

Definitions Center – the center of the circle circumscribed about the polygon radius – a segment drawn from the center of a polygon to a vertex apothem – a segment drawn from the center of a polygon that is perpendicular to a side central angle – an angle formed by two radii drawn to consecutive vertices radius center apothem Central angle

Theorem 11.6 Area of a Regular Polygon The area of a regular n-gon with side lengths (s) is half the product of the apothem (a) and the perimeter (P), so A = ½ aP, or A = ½ a ns. NOTE: In a regular polygon, the length of each side is the same. If this length is (s), and there are (n) sides, then the perimeter P of the polygon is n s, or P = ns The number of congruent triangles formed will be the same as the number of sides of the polygon.

More... A central angle of a regular polygon is an angle whose vertex is the center and whose sides contain two consecutive vertices of the polygon. You can divide 360° by the number of sides to find the measure of each central angle of the polygon. 360/n = central angle

Ex: Finding the area of a regular polygon A regular pentagon with radius 1 unit. Find the area of the pentagon. B C A 1 1 D

Solution: you must find the apothem (or if the apothem was given, you must find the radius, etc) You need to find measure of central angle.  ABC is 360°/5, or 72°.

Solution: Draw the apothem. It is an isosceles triangle so it bisects the angle. You now have a right triangle and can use trig ratios to find the missing sides 36 °

Solution

You try….. Find the area of a regular polygon with 9 sides and a radius of 10