PRISM

Prism is a polyhedron in which two faces are equal polygons in parallel planes, and all other faces are parallelograms. There are two types of prism; oblique prism and right prism. Oblique prism is when the axis is not perpendicular to the base and right prism if the axis is parallel to the base. In right prism, all lateral areas are rectangle.

ELEMENTS OF A PRISM

ELEMENTS OF A PRISMBase - Prism has two equal parallel bases, the upper

and lower base. The area of the base is denoted by Ab.

Altitude - The perpendicular distance between the upper and lower bases and is denoted by h.

Axis - The line that connects the centroid of upper and lower bases. The length of axis is equal to the length of the lateral edge.

Lateral Area - Area of the side of the prism, it is denoted by Al.

Lateral Edge - Lateral edge or lateral side is a line that connects the corresponding vertices of the bases. Edge in general is the line made by the intersection of two lateral faces.

Right Section - Right section is the section made by a cutting plane that is perpendicular to the axis of the prism. The area of the right section is denoted by Ar.

Vertex - Vertex is a point formed by the intersection of three or more edges. Note that at least three edges must intersect to define the vertex of a solid.

IMPORTANT PROPERTIES OF A PRISM

The lateral faces of a prism are either rectangles or parallelograms. If each base of a right prism is a regular polygon of sides, the prism contains number of congruent lateral faces which are rectangles

The sections of a prism made by parallel planes intersecting all lateral edges are congruent polygons.

The bases of a prism are congruent polygons.Every section made by a plane parallel to the base is

congruent to the base.The lateral edges of a prism are parallel and equal.

FORMULASSURFACE AREA OF A PRISM

The lateral surface area (or simply lateral area) of a prism is the sum of the areas of all its lateral faces. Generally, it is the product of the perimeter of a right section and the length of a lateral edge.

where is the lateral surface area, is the perimeter of the right section and is the length of a lateral edge.

The total surface area may be computed as

where is the total surface area, is the lateral surface area and is the base area.

VOLUME OF A PRISMThe volume of a prism is the amount of space it

occupies. The general formula for volume of a prism is

where is the base area and is the height of the prism.

You may solve for the area of the base using the appropriate formula in finding the area of the base polygon. For oblique prism, the volume is

where is the area of a right section and is the length of a lateral edge with the inclination measured with respect to plane B. Since and , then .