Geometry: An Interactive Journey to Mastery



Formulas

DUHDRIDSRO\JRQ6XEGLYLGHLQWRWULDQJOHV

area of a regular NJRQ6XEGLYLGHNWULDQJOHVHDFKZLWKLWVDSH[DWWKHFHQWHURIWKHSRO\JRQ

Circles

The equation of a circle with center C ͼ௘a, b௘ͽDQGUDGLXVrLVͼ௘xía௘ͽ^2 ͼ௘yíb௘ͽ^2 = r^2 ͼ௘7KLVLVMXVWDQ

DSSOLFDWLRQRIWKH3\WKDJRUHDQWKHRUHP௘ͽ

If C is the circumference of a circle, D is its diameter, rLVLWVUDGLXVͼ௘WKXVD = 2r௘ͽDQGA is its area, then

S CD.

Cr^ 2.S

Ar^ S^2.

If an arc of the circle of radius r has measure xƒWKHQWKHOHQJWKRIWKHDUFLV 360 x ˜2.Sr

7KHDUHDRIWKHVHFWRUGH¿QHGE\WKDWDUFLV 360 x ˜Sr^2.

Volumes and Surface Areas

YROXPHRIDF\OLQGHUULJKWRUREOLTXH

V DUHDEDVHîKHLJKW

 ͼ௘6HHFigure F.1௘ͽ

volume of a cone

V =^13 DUHDEDVHîKHLJKW

 ͼ௘6HHFigure F.2௘ͽ

h

Figure F.1

Figure F.2