PREPARING Become a MATIZEN What is Math Planet ? A Crash Course on      Algebra A Crash Course on      Geometry   EXPLORING Advanced Math Topic Customized Lessons SAT & ACT Reviews   INTERACTING Math Games Discussion Forum Math Live! Chat   COLLECTING Math Search MATIZEN Qualifi-      -cation Test Acknowledgements The Creatures Behind      the Math Planet     ©1998 ThinkQuest team 16284 All rights reserved

# Part 10

 Theorem 12.4 The area of a kite is one-half the product of the lengths of the diagonals (Area of kite = 1djd2). Corollary The area of a rhombus is one-half the product of the lengths of the two diagonals. Theorem 12.5 If s is the length of a side of an equilateral triangle, then the area is s^2Ö 3/4 Theorem 12.6 Heron's Formula. If a, b, and c are the lengths of the sides of a triangle and s is the serniperimeter, such that s = 1/2(a + b + c), then Area(triangle) = Ö s(s- a)(s - b)(s - c). Theorem 12.7 The area of a trapezoid is one-half the product of the sum of the lengths of the upper and lower bases and the length of an altitude. Theorem 12.8 A circle can be circumscribed about any regular polygon. Theorem 12.9 The area of a regular polygon is one-half the product of the apothem and the perimeter [Area (n-gon) = 1/2ap)]. Theorem 12.10 The area of a regular polygon is n[sin(18-0)] [cos(180 ]r 2, orns2 180 , where n is the number of sides, s is the length of a 4 tan (T) side, and r is the length of a radius. Theorem 12.11 The ratio of the perimeters of two similar polygons is the same as the ratio of the lengths of any two corresponding sides. Theorem 12.12 The ratio of the areas of two similar triangles is the square of the ratio of the lengths of any two corresponding sides. Theorem 12.13 The ratio of the areas of two similar polygons is the square of the ratio of the lengths of any two corresponding sides. Theorem 12.14 The ratio of the circumference to the length of a diameter is the same for all circles. Corollary The circumference of a circle with radius of length r is 2rP. Theorem 12.15 The area of a circle with radius of length r is Pr^2 Theorem 12.16 The area of a sector of a circle is one-half the product of the length s of the arc and the length r of its radius (A = 1/2rs). Theorem 13.1 The locus of points in a plane equidistant from two given points is the perpendicular bisector of the segment having the two points as endpoints. Theorem 13.2 In a plane, the locus of points equidistant from the sides of an angle is the bisector of the angle. Theorem 13.3 The perpendicular bisectors of the sides of a triangle are concur- rent at a point equidistant from the vertices of the triangle. Theorem 13.4 The bisectors of the angles of a triangle are concurrent at a point equidistant from the sides of the triangle.

.

Note: The concepts in this collection may not be entirely accurate.
They are for reference only.