# 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.
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 A = 1/2(bh), where b is the length of the base, and h is the length of the altitude. 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. 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.

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