Geom11 Whirwind Tour
- 1. Chapter 11 - Area of Polygons & Circles - Whirlwind Tour Objectives: Find angle measures and areas of polygons Find the area and circumference of a circle and of parts of a circle.
- 2. Polygon Interior Angles What is the sum of the measure of interior angles of these?
- 3. Polygon Interior Angles How would you calculate the sum of the interior angles of a pentagon?
- 4. Polygon Interior Angles How would you calculate the sum of the interior angles of a pentagon? Make triangles!
- 5. Polygon Interior Angles How would you calculate the sum of the interior angles of a pentagon? Make triangles!
- 6. Polygon Interior Angles Theorem The sum of the measures of the interior angles of a convex n-gon is (n-2)*180˚ Try this for a pentagon. The measure of each interior angle of a regular n-gon is (n-2)* 180˚ n
- 7. Polygon Exterior Angles Theorem The sum of the measures of the exterior angles of a convex n-gon, one angle at each vertex, is 360˚ The measure of each exterior angle of a regular n-gon is 360˚ n
- 8. Area of an equilateral triangle A = 1/4√3s 2 If a triangle has sides that are 4 inches long, what is the area? 1/4 * √3*4*4 = 4 * √3 inches
- 9. Area of a Regular Polygon 1/2 aP where a is the apothem P is the perimeter of the base The apothem is the distance from the center to any side of the polygon:
- 10. Finding the Apothem of a Hexagon Review: A 30-60-90 triangle has sides in the ration of 1, 2, √3 The apothem of a hexagon creates a 30-60-90 triangle. If each side is 5, what is the apothem? Radius is 5 Half side is 2.5 Apothem is 2.5 √3
- 11. Finding the Apothem of a Pentagon This pentagon has sides that are each 1 foot long. The measure of each of the angles is 360˚/5 = 72˚ The measure of half of this angle is 36˚. The cos 36˚ = adj/hyp = apothem/1 = apothem
- 12. Circumference of a Circle 2πr
- 13. Arc Length The ratio of the length of a given arc to the circumference is equal to the ratio of the measure of the arc to 360˚ If the arc is 50˚ and the radius is 5, the arc length is 2π*5*50/360 = 4.36
- 14. Area of a Circle πr 2
- 15. Area of a sector The ratio of the area of a sector of a circle to the area of the circle is equal to the ratio of the measure of the intercepted arc to 360˚ If the intercepted arc is 80˚ and the radius is 4, the arc length is π*4*4*80/360 = 11.17