Chapter 11
Area of Polygon Formula
A = 1/2 Pa
Right Prism
A geometric solid that has polygons as its bases and each side is a rectangle that is perpendicular to both bases. The volume of any right prism or right cylinder is Area of the Base times height. V = Bh
Edge
A line segment formed when two faces meet
Vertex of a Polyhedron
A point where three or more faces meet
Pyramid
A polyhedron with a polygon base and line segments connecting the vertices of the base with a single point called the vertex of the pyramid
Regular Polyhedron
A polyhedron with faces that are congruent regular polygons
Prism
A polyhedron with two congruent polygons in parallel planes as bases
Geometric Probability
A ratio that involves geometric measure such as length or area
Sphere
A set of all points in space that are equidistant from a given point called center.
Polyhedron
A solid bounded by polygons called faces
Central angle of Regular Polygon
An angle formed by two radii drawn to consecutive vertices of the polygon.
Probability and Area
If a point K in J is chosen at random, then the probability that it is in region M is the ratio of the Area of M to the area of J P(K is in region M) = Area of M/Area of J
Probability and Length
If a point K on AB is chosen at random, then the probability that it is on CD is the ratio of the length of CD to the length of AB P(K is on CD) = Length of CD / Length of AB
Volume Congruence Postulate
If two polyhedrans are congruent, then they have the same volume.
Similar Solids Theorem
If two similar solids have a scale factor of a:b then corresponding areas have a ratio of a^2:b^2 and corresponding volumes have a ratio of a^3:b^3
Cavalieri's Principle
If two solids have the same cross-sectional area at every level, then they have the same volume.
Sector of a Circle
Is the region bounded by two radii of the circle and their intercepted arc. It's a slice of the circle.
Area of a Circle
The area of a circle is π times the square of the radius. The area is the 2D volume of a shape.
Area of a Regular Polygon
The area of a regular n-gon with the side length is one-half the product of the apothem a and the perimeter P.
Lateral Area
The area of the faces of a solid NOT including the bases
Center of Polygon
The center of the polygon's circumscribed circle.
Circumference of a Circle
The circumference of a circle is the whole measure of the line making the circle. The equation to solve for the circumference of a circle is C = πd | C = 2πr
Apothem of Polygon
The distance from the center to any side of the polygon.
Slant Height
The height of each triangular lateral face.
Great Circle
The intersection of a sphere and a plane that contains the center of the sphere * Circumference of great circle = Circumference of sphere * A great circle divides a sphere into two hemispheres
Arc Length Corollary
The length of an arc is part of the circumference. The formula to find the measure of the arc is ARC = mARC/360 * 2πr
Probability
The likelihood that an event will occur - It is a number between 0 and 1 or a percentage between 0% and 100%
Euler's Theorem
The number of faces (F), vertices (V), and edges of (E) of a polyhedron are related by the formula F + V = E + 2
Radius of a Polygon
The radius of the polygon's circumscribed circle.
Area of a Sector
The ratio of the area of a sector of a circle to the area of the whole circle (πr²) is equal to the ratio of the measure of the intercepted arc to 360.
Scale Factor
The ratio of the lengths of two corresponding sides of similar figures.
Surface Area
The sum of the areas of all the faces or surfaces that enclose a solid
Surface Area of a Sphere
The surface area S of a sphere is S = 4πr^2
Volume of a Cone
The volume V of a cone is V = 1/3 Bh = 1/3πr^2h
Volume of a Cylinder
The volume V of a cylinder is V = Bg = πr^2*h
Volume of a Prism
The volume V of a prism is V = Bh
Volume of a Pyramid
The volume V of a pyramid is V = 1/3Bh.
Volume of a Sphere
The volume V of a sphere is V = 4/3πr^3
Volume of a Cube Postulate
The volume of a cube is the cube of the length of its side. V = S^3
Classifying Solids
To name a prism or pyramid, use the shape of the base. Ex: Pentagonal Prism
Similar Solids
Two solids of the same type with equal ratios of corresponding linear measures.
