1. Objectives
Develop and apply the formulas for the area and circumference of a circle.
Develop and apply the formula for the area of a regular polygon.

2. A ______ is the locus of points in a plane that are a fixed distance from a point called the ______________. A circle is named by the symbol  and its center. A has radius r = ___ and diameter d = ____.
The irrational number 
is defined as the ratio of
the circumference C to
the diameter d, or
Solving for C gives the formula
C = ____. Also d = ____, so C = ____.

3. You can use the circumference of a circle to find its area
You can use the circumference of a circle to find its area. Divide the circle and rearrange the pieces to make a shape that resembles a parallelogram.
The base of the parallelogram is about half the circumference, or r, and the height is close to the radius r. So A   r · r =  r2.
The more pieces you divide the circle into, the more accurate the estimate will be.

5. Example 1A: Finding Measurements of Circles
Find the area of K in terms of .

6. Always wait until the last step to round.
The  key gives the best possible approximation for  on your calculator.
Always wait until the last step to round.
Helpful Hint

7. Example 2: Cooking Application
A pizza-making kit contains three circular baking stones with diameters 24 cm, 36 cm, and 48 cm. Find the area of each stone. Round to the nearest tenth.
24 cm diameter
36 cm diameter
48 cm diameter

8. _________ – A segment that is drawn from the center of a regular polygon perpendicular to a side of the polygon.
__________– An angle formed by two segments drawn to consecutive vertices of a regular polygon from its center. C.A.
, where n = # of sides.
_____________________– A =
Pa,
where P = _______ and a = ________.

9. Regular pentagon DEFGH has a center C, apothem BC, and central angle DCE.

10. To find the area of a regular polygon:3. 4.

11. Example 3A: Finding the Area of a Regular Polygon
Find the area of regular heptagon with side length 2 ft to the nearest tenth.
Step 1 Draw the heptagon. Draw an isosceles triangle with its vertex at the center of the heptagon. The central angle is
Draw a segment that bisects the central angle and the side of the polygon to form a right triangle.

12. Example 3A Continued
Step 2 Use the tangent ratio to find the apothem.

13. Example 3A Continued
Step 3 Use the apothem and the given side length to find the area.

14. Check It Out! Example 3B
Find the area of a regular octagon with a side length of 4 cm.
Step 1 Draw the octagon. Draw an isosceles triangle with its vertex at the center of the octagon. The
central angle is
Draw a segment that bisects the central angle and the side of the polygon to form a right triangle.

15. Check It Out! Example 3B Continued
Step 2 Use the tangent ratio to find the apothem

16. Check It Out! Example 3B Continued
Step 3 Use the apothem and the given side length to find the area.