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Triangles

Central Angle. Triangles. Interior Angle. r. Triangles. apothem. r. Find: Central Angle. Triangles. Whole circle is 360 0. There are 3 angles that make up 360 0 thus Measure of central angle is = 360/3. Central Angle of triangle =120 0. To find: Interior Angle Measure of central=120

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Triangles

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  1. Central Angle Triangles Interior Angle

  2. r Triangles apothem r

  3. Find: Central Angle Triangles Whole circle is 3600 There are 3 angles that make up 3600 thus Measure of central angle is = 360/3 Central Angle of triangle =1200

  4. To find: Interior Angle Measure of central=120 Sum of all angles in the blue triangle is 180 Triangles each side angle will be = (180-120)/2 = 300 Interior Angle Interior Angle= 2* 300 = 600

  5. r 60 Triangles r/2 apothem 30 r r√3/2 Side Length = 2 * r√3/2 = r√3 Perimeter = 3*side length = 3r√3

  6. Triangles r/2 r√3 Total Area = 3*Area of ORANGE TRIANGLE = r2 (3/4)√3 Area ORANGE TRIANGLE= ½b*a=½ r√3*r/2= (r2/4)√3

  7. Find: Central Angle Whole circle is 3600 There are 4 angles that make up 3600 thus Measure of central angle is = 360/4 = 900 Square

  8. Find: Internal Angle = 2* [180-90]/2 = 180-90 = 900 Square

  9. r Square Apothem = r√2/2 r 45 r/√2 45 Side Length = 2 * r√2/2 = r√2 r/√2= r√2/2 Perimeter = 4*side length = 4r√2

  10. Square 45 r√2/2 45 r√2 = 2r2 Total Area = 4*Area of BLUE TRIANGLE Area BLUE TRIANGLE=½b*a=½ r√2*r√2/2= (r2/2)

  11. Apothem= .80802r r

  12. Apothem= . 9239r r

  13. Apothem r

  14. http://www.mathopenref.com/polygonapothem.html

  15. Ex 1.) Find the area of the pentagon with apothem=3 & radius 5.

  16. Ex 2.) Find the area of the hexagon with side length = 4. 4

  17. Ex 3.) Find the shaded & un-shaded region of the equilateral triangle with side length 2 inscribed in the circle.

  18. Ex 4.) Given 3 shapes: A square with diagonal length = 6, A regular hexagon with diagonal length= 6, and a circle with diameter equal to 6. Which of the following is true. • Area Square < Area hexagon < Area Circle • Area Square > Area hexagon > Area Circle • Area Square = Area hexagon = Area Circle • Area Square > Area Circle > Area hexagon • It is impossible to tell from the information given

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