 Find areas of regular polygons.  Find areas of circles.

 Apothem- A segment drawn from the center of a regular polygon perpendicular to a side of the polygon  Apothem=a or BD

 Triangle ABC is an isosceles triangle, since the radii are congruent. If all of the radii were drawn, they would separate the hexagon into 6 nonoverlapping congruent isosceles triangles BA C D

Area of a triangle is A=1/2(base)(height) The height of the triangle is equal to a and the base is s then ½ bh= ½ sa The total area of the hexagon is 6( ½ sa) Perimeter is 6s so A=6( ½ sa) becomes A= ½ Pa BA D C a s

 Find the area of a regular hexagon with a perimeter of 60

Central angles of a regular pentagon are all congruent. Therefore, the measure of each angle is 360/6 or 60. BD is an apothem of the hexagon. It bisects angle ABC and is a perpendicular bisector to AC. So measure of angle CBD= ½ (60) or 30. Since the perimeter of hexagon is 60 each is 10 units long and DC=5 units. Tan CBD= DC/BD Tan 30 = 5/BD (BD) tan 30 =5 BD=5/tan 30 BD 8.7 A= ½ Pa = ½ (60)(8.7) A=261

 Area of a circle= πr Find the area of the shaded region 2 4

The area of the shaded region is the difference between the area of the circle and the area of the triangle. First, find the area of the circle. A= πr = π(4)

To find the area of the triangle, use properties of triangles. First, find the length of the base. The hypotenuse of ABC is 4, so BC is 2 √3. Since EC= 2(BC), EC=4 √ A B CE D

Next, find the height of the triangle, DB. Since m DCB is 60, DB= 2 √3(√3) or 6. A= ½ bh = ½ (4 √3)(6) 20.8 The area of the shaded region is or 29.5 square units to the nearest tenth. 60 A B CE D 2 √3

Pg. 613 #8 – 22, 26 – 32 evens

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