sparknotes
Geometry: 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.
, 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 |
|
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