11-3 Areas of Regular Polygons and Circles

11-3Areas of Regular Polygons and Circles

Objectives • Find areas of regular polygons • Find areas of circles

Find Areas of Regular Polygons

A Definition… Apothem – a segment that is drawn From the center of a regular polygon Perpendicular to the side of the polygon. If all radii were drawn, there would be 6 congruent isosceles triangles. An area of a hexagon is determined by adding areas of the triangles inside. A B H F G C E D

A Formula… • Area of a triangle = ½bh = ½sa If the area of a triangle = ½sa, then the area of a hexagon = 6(½sa)

Example #1… Find the are of a regular pentagon with a perimeter of 40 cm. K P J L P N Q M

TAN angle MPQ = QM / PQ TAN 36 = 4 / PQ PQ = 4 / TAN 36 PQ ~ 5.5 ½ (40)(5.5) = A ~110 So the area of the pentagon is about 110 centimeters.

Find Areas of Circles

Area of a Circle… • Area of a circle = r²

Example #2… A caterer has a 48-inch diameter table that is 34 inches tall. She wants a tablecloth that will touch the floor. Find the area of the tablecloth. 48 in 34in

34 + 48 + 34 = ll6 divided by 2 = 58 so the radius = 58. • A = pi(58)² • ~ 10,568

Example #3… • Find the area of the shaded region. Assume that the triangle is equilateral. 4m

A = pi(4)² ~ 50.3 – area of circle Use 30-60-90 rules AB = 2 BC = 2√3 DB = 2√3(√3) = 6 A = ½ (4√3)(6) ~20.8 50.3 – 20.8 =29.5 m²

Assignment… • Page 613 • #’s 8 – 23, 26

Questions? Thank you! Laura Beth Stover Connor Reece

11-3 Areas of Regular Polygons and Circles