1. LESSON 7.5
AREAS OF REGULAR POLYGONS
OBJECTIVE:
To find the area of regular polygons

2. REMINDER:
A REGULAR POLYGON HAS
All sides  and all angles  .

3. All REGULAR POLYGONS HAVE
a circumscribed circle

4. PARTS OF A POLYGON
Center of a regular polygon is the
center of the circumscribed circle.

5. Radius of a regular polygon is the
distance from the center to a vertex.
Apothem of a regular polygon is the
 distance from the center to a side.

6. 360 n All ’s are  and isos. The measure of each vertex  is: apothem
radius
center
360
The measure of each vertex  is: n

7. A = ½ asn AREA OF REGULAR POLYGONS Is half the product of the
times the length of a
times the number of
apothem (a),
side (s),
sides (n),
A = ½ asn

8. p = ns A = ½ ap (n) times (s) equals the perimeter of the polygon so:
An alternative formula
for area of a polygon would be:
A = ½ ap

9. A = ½ asn A = ½(3.2)(4)(7) A = 44.8 m2 Example #1
Find the area of a regular heptagon if the
apothem = 3.2m and the length of a side
is 4m.
A = ½ asn
A = ½(3.2)(4)(7)
A = 44.8 m2

10. A = ½ ap 182 = ½(7)p 182 = 3.5p 52 cm = p Example #2
1.  Find the perimeter of a regular polygon if
the apothem = 7cm and the area = 182cm2.
A = ½ ap
182 = ½(7)p
182 = 3.5p
52 cm = p

11. ASSIGNMENT:
7.5 Worksheet
Show necessary work
Minimum 3 lines