1. 3-18-15 Areas, Surface Areas, and Volumes Unit Areas of Regular Polygons

2. Things to Remember Remember: 30-60-90 triangles shortcuts H = (SL ) 2 LL = ( SL )√ 3 Trig Ratios : Angles of a Polygon

3. Terms to Know: Any regular polygon : Radius : is a segment joining the center to any vertex Apothem : is a segment joining the center to the midpoint of any side and is also perpendicular to the side.

4. Area of a regular polygon: Remember all angles are congruent and all sides are congruent. Regular pentagon: O is the center OA the radius OM is an apothem N T A O M E P

5. Apothems Facts : 1.All apothems of a regular polygon are congruent. 2.Only regular polygons have apothems. 3.An apothem is the perpendicular bisector of a side.

6. A reg. poly = ½ a p Area of a regular polygon equals one-half the product of the apothem and the perimeter. Where : a = apothem p = perimeter

7. A regular polygon has a perimeter of 40 cm and an apothem of 5 cm. Find the polygon’s area. A = ½ap = ½(5)(40) = 100 cm 2

8. Find the area of a regular hexagon whose sides are 18 cm long. 1. Draw the picture 2. Write the formula 3. Plug in the numbers 4. Solve and label units

9. 18cm Find the perimeter Find each angle Find the apothem Write the formula, and solve. P = 18(6) = 108 cm Angles = 720 º /6 angles = 120 º per angle Radius breaks it into 60 º angles. 30-60-90 triangle, apothem = 9 √ 3 cm A = ½ ap A = ½ (9 √ 3)108 A = 486 √ 3 cm 2