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Agenda

Agenda. 1 st block 45-45-90 and 30-60-90 triangle worksheet Notes 11-4 Classwork due by end of class. 3 rd block Pop quiz Go over homework from Wednesday night Notes 11-4 Classwork due by end of class. Areas of Regular Polygons. 11-4. Goals/Purpose.

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Agenda

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  1. Agenda • 1st block • 45-45-90 and 30-60-90 triangle worksheet • Notes 11-4 • Classwork due by end of class • 3rd block • Pop quiz • Go over homework from Wednesday night • Notes 11-4 • Classwork due by end of class

  2. Areas of Regular Polygons 11-4

  3. Goals/Purpose • At the completion of the lesson, you will be able to… • identify and calculate the center, radius, apothem, and central angle of a regular polygon • Calculate the area of a regular polygon • We are studying this material because regular polygons are common in structures and buildings

  4. 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

  5. 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.

  6. 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

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

  8. 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°.

  9. 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°

  10. Solution

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

  12. Homework • Page 442 1-8

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