Honors Geometry Sections 6.3 & 7.2 Surface Area and Volume of Prisms

In the previous section, we discussed surface area and volume of boxes In the previous section, we discussed surface area and volume of boxes. A box is a special type of a more general group of 3-dimensional objects called prisms. Before we discuss prisms, we need to discuss an even more general type of 3-dimensional object called a polyhedron.

A polyhedron is a 3-dimensional figure made up of polygons A polyhedron is a 3-dimensional figure made up of polygons. Each polygon is called a ______ and the line segment formed by the intersection of two faces is called an ______. The point where the edges intersect is called a _______ face edge vertex.

A prism is a polyhedron where two faces are parallel congruent polygons whose corresponding sides are joined by parallelograms.

The faces formed by the parallel polygons are called the ______ of the prism (think of these as the top and bottom of the prism). The remaining faces (i.e. the parallelograms) are called the ___________of the prism. The line segments forming the bases are called ___________while the line segments formed by the intersection of two lateral faces are called ____________ bases lateral faces base edges lateral edges.

base lateral edge lateral face base edge

Prisms are name by the shape of their bases. triangular rectangular pentagonal hexagonal

The lateral faces give us an additional classification for prisms The lateral faces give us an additional classification for prisms.   A  right prism is a prism in which all lateral faces are _________. An oblique prism has at least one ______________ lateral face. You should always assume a prism is a right prism unless told otherwise. rectangles non-rectangular

An altitude of a prism is a segment that has an endpoint in each base of the prism and is perpendicular to the bases. The height of a prism is the length of the altitude. Note: In a right prism a lateral edge will be an altitude.

We look at the surface area of a prism in two parts: the area of the lateral faces and the area of the bases.

If we unfold the right prism above it would look like this: This “unfolded” representation of a 3-dimensional object is called a _____.   Area rect. I = _____ Area rect. II = _____   Area rect. III = _____   Lateral Area = ____________ = ____________ net ah bh ch ah + bh + ch h( a + b + c)

Lateral Area of a Prism = perimeter of the base X height of the prism

Surface Area of a Prism = lateral area + 2(area of a base)

Volume of a Right Prism = area of a base X height of the prism

Example 1: A right regular hexagonal prism has base edges of length 14 in. and height of 48 in. Find its surface area and its volume.

Example 1: A right regular hexagonal prism has base edges of length 14 in. and height of 48 in. Find its surface area and its volume.