1. Areas, Surface Areas, and Volumes Unit
Areas of Regular Polygons

2. Things to Remember Trig Ratios : Angles of a Polygon
Remember: triangles shortcuts
H = (SL ) 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. N
Regular pentagon:
O is the center
OA the radius
OM is an apothem O T E P M A

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

6. A reg. poly = ½ a p Where : a = apothem p = perimeter
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
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

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

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