WARM UP 1)Find the area of a trapezoid with bases 8 and 11 and a height of )Find the area of an equilateral triangle with sides 8ft. 3)An isosceles trapezoid has bases 12 and 28. The area is 300. Find the height and the perimeter. 4)Find the area of a rhombus with a 120 o angle and sides of 6 cm.

Section 11.4 AREAS of REGULAR POLYGONS

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.

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

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

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

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

SIMPLE 2)Find the area a regular octagon with side 5 and apothem 3. A= ½ ap A= ½ (3)p P = 5(8) P = 40 A= ½ (3)(40) A= 60

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

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

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

PRACTICE Page 442 # Classroom Exercises Draw Diagrams