Transcript Area Regular Polygons

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