1. Area of Regular Polygons 5.5

2. Learn the vocabulary associated with regular polygons.
Find the area of regular polygons.

4. Center of a polygon – the center of its circumscribed circle.
Radius of a polygon – the radius of its circumscribed circle, or the distance from the center to a vertex.
Apothem of a polygon – distance from the center to any side of the polygon.

5. The area of a regular n-gon with side length
s is half the product of the apothem a and
the perimeter P.

6. Find another way to find the area of the regular hexagon shown.
Find the area of one of the triangles and multiply by six.

7. In the diagram, ABCDE is a regular pentagon inscribed in circle F
In the diagram, ABCDE is a regular pentagon inscribed in circle F. Find each angle measure.

8. Lets start with an equilateral triangle given an apothem.
Find the perimeter and area of the regular polygon.
Draw the radius, find the central angle. Divide the central angle in half and solve the triangle.
The central angle is 360 divided by the number of sides. Divide this in half and label it.
Find the side lengths using the rule.
Find the perimeter.
60 10
Apply the formula.

9. Now try an equilateral triangle given a side.
Find the perimeter and area of the regular polygon.
Draw the altitude. Solve the triangle.
Find the side lengths using the rule. 8
Find the perimeter.
Apply the formula.

10. Now try an equilateral triangle given a radius.
Find the perimeter and area of the regular polygon.
Draw the apothem, find the central angle. Divide the central angle in half and solve the triangle.
The central angle is 360 divided by the number of sides. Divide this in half and label it.
60
Use the rule. 2
Find the perimeter.
Apply the formula.

11. 10 Now try a square given a radius.
Find the perimeter and area of the regular polygon.
Draw the diagonal, find the area. Use special right triangle to find the side and determine the perimeter.
Apply the formula. 10
Find the side length using the rule.
Find the perimeter.

12. Now try a square given an apothem.
Find the perimeter and area of the regular polygon.
Find the side, find the area, determine the perimeter. 14
Apply the formula. A = s2
Find the perimeter.

13. Now try a regular hexagon given a radius.
Find the perimeter and area of the regular polygon.
Draw the apothem, find the central angle. Divide the central angle in half and solve the triangle.
The central angle is 360 divided by the number of sides. Divide this in half and label it.
30
Use the rule.
3.5
Find the perimeter.
Apply the formula.

14. Now try a regular hexagon given an apothem.
Find the perimeter and area of the regular polygon.
Find the central angle. Divide the central angle in half and solve the triangle.
The central angle is 360 divided by the number of sides. Divide this in half and label it.
30
Use the rule.
Find the perimeter.
Apply the formula.

15. Now try a regular pentagon given an apothem.
Find the perimeter and area of the regular polygon.
Draw the radius, find the central angle. Divide the central angle in half and solve the triangle.
The central angle is 360 divided by the number of sides. Divide this in half and label it.
36
Use trigonometry.
Find the perimeter.
Apply the formula.

16. You are decorating the top of a table by covering it with small ceramic tiles. The table top is a regular octagon with 15 inch sides and a radius of about 19.6 inches. What is the area?
Find the perimeter P of the table top. An
octagon has 8 sides, so P = 8(15) = 120 inches.
Find the apothem a. The apothem is height
RS of ∆PQR. Because ∆PQR is isosceles,
altitude RS bisects QP .
So, QS = (QP) = (15) = 7.5 inches. 1 2
To find RS, use the Pythagorean Theorem for ∆ RQS.
Apply the formula.
A≈ in²

17. Find the area and perimeter of the regular figure.b. c. d. e. f.

18. Find the area and perimeter of the regular figure.b. c. 12 6 18 d. e. f.

19. Find the area and perimeter of the regular figure.b. c. d. e. f.

20. Find the area and perimeter of the regular figure.b. c. d. e. f.

21. Find the area and perimeter of the regular figure.b. c.

22. Area & Perimeter of Regular Polygons
Assignment
Area & Perimeter of Regular Polygons