 |
 |
|
©1998 ThinkQuest
|
| |
|
|
©1998 ThinkQuest
|
| 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.
PREPARING