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Transcript
3-18-15 Areas, Surface Areas, and Volumes Unit Areas of Regular Polygons Things to Remember Remember: 30-60-90 triangles shortcuts H = (SL ) 2 LL = ( SL )√ 3 Trig Ratios : Angles of a Polygon 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. Area of a regular polygon: Remember all angles are congruent and all sides are congruent. N E Regular pentagon: O T O is the center OA the radius P M A OM is an apothem 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. A reg. poly =½ap Area of a regular polygon equals one-half the product of the apothem and the perimeter. Where : a = apothem p = perimeter 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 cm2 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 Find the perimeter Find each angle Find the apothem 18cm P = 18(6) = 108 cm Angles = 720º/6 angles = Write the formula, 120º per angle Radius breaks it into 60º and solve. angles. 30-60-90 triangle, apothem = 9√3 cm A = ½ ap A = ½ (9√3)108 2 A = 486√3 cm