Developing Formulas for Circles and Regular Polygons
Circumference and Area of Circles
A circle with diameter d and radius r has circumference C d or C 2 r. A circle with radius r has area A
2 r .
Find the circumference of circle S in which A Step 1 Use the given area to solve for r. A 81 cm
2 81 cm .
r2 r r2 r
Area of a circle Substitute 81 for A. Divide both sides by . Take the square root of both sides. cm 81 cm2 9 cm Step 2
Use the value of r to find the circumference. C C 2 r 2 (9 cm) 18 cm Circumference of a circle Substitute 9 cm for r and simplify.
Find each measurement. 1. the circumference of circle B 2. the area of circle R in terms of
6 – cm
3. the area of circle Z in terms of
4. the circumference of circle T in terms of
121 ft 2
5. the circumference of circle X in 2 which A 49 in
6. the radius of circle Y in which C
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Developing Formulas for Circles and Regular Polygons continued
Area of Regular Polygons The center is equidistant from the vertices.
The area of a regular polygon with apothem a and perimeter P 1 is A __aP. 2
The apothem is the distance from the center to a side.
Find the area of a regular hexagon with side length 10 cm. Step 1 Draw a figure and find the measure of a central angle. Each central 360° angle measure of a regular n-gon is ____. n A central angle has its vertex at the center. This central angle measure is 360 ____ 60 . n Step 2 Use the tangent ratio to find the apothem. You could also use the 30°-60°-90° Thm. in this case. tan 30° tan 30° leg opposite 30° angle ____________________ leg adjacent to 30° angle 5 cm _____ Write a tangent ratio. Substitute the known values. Solve for a.