1. 11.5 Areas of Regular Polygons

2. Equilateral Triangle
Remember: drop an altitude and you create two triangles.
What is the measure of the sides and altitude in terms of one side equaling s?

3. Find the altitude (h) of the ∆.C
Given: ∆ CAT is equilateral, and TA = s
Find the area of ∆CAT A T S
Find the altitude (h) of the ∆.
A ∆CAT = = 2

4. T106: Area of an equilateral triangle = the product of 1/4 the square of a side and the square root of 3. Where s is the length of a side 2
Aeq∆ =

5. Area of a regular polygon:
Remember all interior angles are congruent and all sides are equal. N
Regular pentagon:
O is the center
OA the radius
OM is an apothem T E O P M A

6. You can make 5 isosceles triangles in a pentagon.
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.

7. See page 532 for observations
Apothems:
Congruent only in regular polygons.
Radius of a circle inscribed in a polygon.
Perpendicular bisector of a side.

8. A radius of a regular polygon bisects an angle of the polygon.
If all radii are drawn, the polygon is divided into congruent isosceles triangles.
The altitude of each triangle is its apothem.

9. T107: Areg poly = 1/2 ap
Area of a regular polygon equals one-half the product of the apothem and the perimeter.
Where a = apothem
p = perimeter

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

11. Write the formula, and solve.
Find the perimeter
Find each angle
Find the apothem
18cm
Write the formula, and solve.