WARM UP

1. WARM UP • Find the area of a trapezoid with bases 8 and 11 and a height of 7.5. • Find the area of an equilateral triangle with sides 8ft. • An isosceles trapezoid has bases 12 and 28. The area is 300. Find the height and the perimeter. • Find the area of a rhombus with a 120o angle and sides of 6 cm.

2. Section 11.4 AREAS of REGULAR POLYGONS

3. Regular Polygons • Think of a kaleidoscope. • The body of a kaleidoscope is a tube and therefore the images always look inscribed in a circle. • You can inscribe any regular polygon into a circle.

4. What is a regular polygon? • A regular polygon is a polygon with all equal sides and angles.

6. Inscribe a Regular Polygon into a Circle 90o 45o Center Radius Central Angle Apothem 60o

7. APOTHEM • The apothem is the perpendicular distance from the center of the polygon to the side. APOTHEM

8. AREA of a REGULAR POLYGON • Area = one half of the apothem and the perimeter. A= ½ ap Perimeter AREA Apothem

9. SIMPLE • Find the area a regular octagon with side 5 and apothem 3. 5 5 5 A= ½ ap 5 5 A= ½ (3)p A= ½ (3)(40) 3 5 5 P = 5(8) A= 60 5 P = 40

10. MEDIUM 1) Find the area of a regular hexagon with apothem 9 and side length of A= ½ ap A= ½ (9)p 9

11. TOUGH 3) Find the area an equilateral triangle with radius 16. A= ½ ap 60o A= ½ (8)p 16 60o 8 60o 30o

12. REAL TOUGH 4) Find the area a regular hexagon with a side of A= ½ ap 30o 60o 120o

13. PRACTICE • Page 442 • # 2 - 8 • Classroom Exercises • Draw Diagrams