9­2 Developing Formulas for Circles and Regular Polygons
A. Circles
1. A circle is the locus of points in a plane that are a
fixed distance from a point called the center the circle.
a. A circle is named by the symbol and its
center.
b. has radius r= AB and diameter d= CD
2. The irrational number π (pi) is defined as the ratio of the circumference C the diameter d, or π = .
a. Solving for C, C = πd or C = 2πr (since d = 2r).
3. Circumference and Area of Circles
A circle with diameter d and radius r has circumference C = πd or C = 2πr and
Area A= πr2
4. Example 1­­finding measurements circles
Find each measurement.
a. The area of K in terms of π
b. The radius of J if the circumference is (65x + 14)π m.
c. The circumference of M if the area is 25x2π
ft2.
5. Example 2
{do not copy} 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 10th.
B. Regular Polygons
1. The center of a regular polygon is equidistant from
the vertices.
2. The apothem is the distance from the center to a side.
3. A central angle of a regular polygon has vertex at the center, and it sides pass­through
consecutive vertices.
a. Each central angle measure of a regular n­gon
is 360°/n.
4. Find the area of a regular n­gon with side length s and apothem a, divide it into n congruent isosceles triangles.
a. area of each triangle : ½as
total area of the polygon: A = n(½as), or
A = ½aP (where ns = Perimeter (P))
5. Area of regular polygons
The area of a regular polygon with apothem a
and perimeter P is A = ½aP
6. Example 3­­finding the area of a regular polygon
Find the area of each regular polygon to the
nearest 10th.
a. A regular heptagon with side length 2 feet
b. A regular dodecagon with side length 5 cm