Geometry - Unit #14 Key Terms

regular pyramid

The base is a polygon (a straight-sided flat shape). The sides are triangles which meet at the top (the apex). It is a polyhedron. This is a square pyramid, but there are also triangular pyramids, pentagonal pyramids, and so on.

lateral area

The lateral surface area is finding the area of the sides of a three-dimensional geometric figure. The formulas for the lateral surface area are based on the base of the figure and whether the figure is a prism, cone, or pyramid.

slant height

The slant height of an object (such as a frustum, or pyramid) is the distance measured along a lateral face by the base to the apex along the "center" of the face. In other words, it is the altitude of the triangle comprising a lateral face.

cone

A cone is a three-dimensional geometric shape that tapers smoothly from a flat base (frequently, though not necessarily, circular) to a point called the apex or vertex.

right cone

A cone whose surface is generated by lines joining a fixed point to the points of a circle, the fixed point lying on a perpendicular through the center of the circle. Compare oblique circular cone.

composite space figure

A figure (or shape) that can be divided into more than one of the basic figures is said to be a composite figure (or shape). For example, figure ABCD is a composite figure as it consists of two basic figures. That is, a figure is formed by a rectangle and triangle.

lateral face

Prisms are three-dimensional closed surfaces. A prism has two parallel faces, called bases, that are congruent polygons. The lateral faces are rectangles in a right prism or parallelograms in an oblique prism. In a right prism, the joining edges and faces are perpendicular to the base faces.

surface area

The total area of the surface of a three-dimensional object. Example: the surface area of a cube is the area of all six faces added together. The formula is 6 × (Edge Length) 2.

volume

Volume is the measure of the amount of space inside of a solid figure, like a cube, ball, cylinder or pyramid. Its units are always "cubic", that is, the number of little element cubes that fit inside the figure.

great circle

A circle defined as the intersection of the surface of a sphere and a plane which passes through the centre of the sphere. A segment of such circle representing the shortest distance between two points on the surface of a sphere.

similar solids

A pair of three-dimensional figures is classified as similar solids when they are the same shapes and their corresponding measurements are proportional. The ratio that compares the measurements of two similar solids is called the scale factor.

polyhedron

A polyhedron (plural polyhedra or polyhedrons) is a solid in three dimensions with flat polygonal faces, straight edges, and sharp corners or vertices.

prism

A prism is a solid object with two identical ends and flat sides. The sides are parallelograms (four-sided shape with opposites sides parallel). The cross section is the same all along its length. The shape of the ends give the prism a name, such as "triangular prism". It is also a polyhedron.

oblique prism

A prism with bases that are not aligned one directly above the other. Note: The lateral faces of an oblique prism are parallelograms.

right prism

A right prism is a geometric solid that has a polygon as its base and vertical sides perpendicular to the base. The base and top surface are the same shape and size. It is called a "right" prism because the angles between the base and sides are right angles.

sphere

A sphere is a geometrical figure that is perfectly round, three-dimensional and circular—like a ball. Geometrically, a sphere is defined as the set of all points equidistant from a single point in space.

oblique cylinder

An oblique cylinder is one that 'leans over"—where the sides are not perpendicular to the bases. Opposite of a 'right cylinder'.

right cylinder

Base and side. A cylinder is a geometric solid that is very common in everyday life, such as a soup can. If you take it apart you find it has two ends, called bases, that are usually circular. The bases are always congruent and parallel to each other.

center of a sphere

Geometrically, a sphere is defined as the set of all points equidistant from a single point in space. The distance from an outer point to the center of the sphere is the radius (r) and the maximum straight distance from one side of the sphere to another is the diameter (d).

diameter of a sphere

Geometrically, a sphere is defined as the set of all points equidistant from a single point in space. The distance from an outer point to the center of the sphere is the radius (r) and the maximum straight distance from one side of the sphere to another is the diameter (d).

height

Height is a measure of a polygon or solid figure, taken as a perpendicular from the base of the figure.

cross section

In geometry and science, a cross section is the intersection of a body in three-dimensional space with a plane or the analog in higher-dimensional space. Cutting an object into slices creates many parallel cross sections.

base

In geometry, a base is a side of a polygon or a face of a polyhedron, particularly one oriented perpendicular to the direction in which height is measured, or on what is considered to be the "bottom" of the figure.

face

In geometry, a face is a flat (planar) surface that forms part of the boundary of a solid object; a three-dimensional solid bounded exclusively by flat faces is a polyhedron.

pyramid

In geometry, a pyramid is a polyhedron formed by connecting a polygonal base and a point, called the apex. Each base edge and apex form a triangle, called a lateral face. It is a conic solid with the polygonal base. A pyramid with an n-sided base will have n + 1 vertices, n + 1 faces, and 2n edges.

vertex

In geometry, a vertex (plural: vertices or vertexes) is a point where two or more curves, lines, or edges meet. As a consequence of this definition, the point where two lines meet to form an angle and the corners of polygons and polyhedra are vertices.

altitude

In geometry, an altitude of a triangle is a line segment through a vertex and perpendicular to (i.e. forming a right angle with) a line containing the base (the opposite side of the triangle). This line containing the opposite side is called the extended base of the altitude.

edge

In geometry, an edge is a particular type of line segment joining two vertices in a polygon, polyhedron, or higher-dimensional polytope. In a polygon, an edge is a line segment on the boundary and is often called a side. In a polyhedron or more generally a polytope, an edge is a line segment where two faces meet.

hemisphere

In geometry, it is an exact half of a sphere. It also refers to half of the Earth, such as the "Northern Hemisphere" (that part of the Earth north of the equator), or "Western Hemisphere" (the half of the Earth west of a line running from the North Pole through England to the South Pole, includes the Americas) Sphere.

radius of a sphere

In geometry, the radius of a circle or sphere is the length of a line segment from its center to its perimeter. The name comes from Latin radius, meaning "ray" but also the spoke of a chariot wheel. The plural of radius can be either radii (from the Latin plural) or the conventional English plural radiuses.

cylinder

When the axis is perpendicular to the plane of the curve, the cylinder is called a right cylinder. In non-mathematical usage, both right and circular are usually implied. (geometry) A solid figure bounded by a cylinder and two parallel planes intersecting the cylinder. Any object in the form of a circular cylinder.

circumference of a sphere

∏ (pi): the ratio of the circumference of a circle to its diameter, approximately 3.14.