SparkNotes Shopping Cart  |     |  Checkout
Brought to you by Barnes and Noble
  Home : Math & Science : Math Study Guides : Geometry II : Measurements : Terms and Formulae
Geometric Measurements
  
 
Terms and Formulae
Terms
Altitude  -  See Altitude of a Parallelogram, Altitude of a Trapezoid, Altitude of a Triangle.
Altitude of a Parallelogram  -  In a parallelogram, the segment with one endpoint on a side and perpendicular to that side, with the other endpoint on the line containing the opposite side
Altitude of a Trapezoid  -  In a trapezoid, the segment with one endpoint on a base and perpendicular to that base, with the other endpoint on the line containing the other base.
Altitude of a Triangle  -  In a triangle, the segment with one endpoint on a vertex, and the other endpoint on the side opposite the vertex, and perpendicular to that side.
Apothem  -  A segment with one endpoint at the center of a regular polygon and the other endpoint at the midpoint of a side.
Area  -  A measurement of the combined length and width of two- dimensional regions.
Base of a Parallelogram  -  A side containing the endpoint of an altitude.
Center of a Regular Polygon  -  The point within a regular polygon that is equidistant from all vertices.
Central Angle of a Regular Polygon  -  An angle created whose vertex is at the center and whose sides (rays) extend through the endpoints of a side.
Circumference  -  The length of the curve that defines a circle.
Heron's Formula  -  A formula that determines the area of a triangle. Named after the mathematician who first proved the formula worked, Heron's Formula is useful only if you know the lengths of the sides of a triangle. Heron's Formula states that the area of a triangle is equal to
, where s is the semiperimeter of the triangle, and a, b, and c are the lengths of the three sides.
Perimeter  -  The length of the simple closed curve or curves that define a region.
Radius of a Regular Polygon  -  A segment with one endpoint at the center and the other endpoint at a vertex of a regular polygon.
Region  -  The collection of points that lie within a simple closed curve.
Semiperimeter  -  One-half of the perimeter.
Square Unit  -  A square whose sides are one unit long.
Formulas
Arc Length L = (n/360)2(pi)r, where n is the measure of the arc in degrees, and r is the radius of the circle.
Area of a Circle A = (pi * radius)2
Area of a Circle Segment A = [(n/360)(pi)(radius)2] - [(1/2)bh], where n is the measure of the arc in degrees, b is the measure of the base of the triangle formed by the radii and the chord, and h is the length of the altitude of that triangle.
Area of a Parallelogram A = bh, where b is the length of the base and h is the length of the altitude.
Area of a Regular Polygon A = 1/2(ap), where a is the length of the apothem and p is the perimeter.
Area of a Rhombus A = 1/2(de), where d and e are the lengths of the diagonals.
Area of a Sector A = (n/360)(pi)(radius)2, where n is the measure of the arc in degrees.
Area of a Square. A = s2, where s is the length of a side.
Area of a Trapezoid A = 1/2(h(b1 + b2), where h is the length of the altitude, and b1 and b2) are the lengths of the bases.
Area of a Triangle
  1. A = 1/2(bh), where b is the length of the base, and h is the length of the altitude.
  2. A = Square root [s(s-a)(s-b)(s-c)], where s is the semiperimeter and a, b, and c are the lengths of the sides of the triangle.
  3. A = 1/2((ab)(sin(C)), where a and b are the lengths of two sides and C is their included angle. Circumference C = 2(pi)r, where r is the length of the radius.
Help | Feedback | Make a request | Report an error | Send to a friend
 
We'll help you raise your score on the SAT II Math IIC test!
More...
 
Get clear, concise lessons from No Fear Math and get caught up.
More...
 
 
Go to top