Finding surface areas and volumes of prisms

1
Finding surface areas and volumes of prisms
2
Surface area of a solid

• Surface area can be considered as the number of
  square units it takes to exactly cover the
  outside of a solid.
• The surface area of a solid is the total area of
  all its faces and curved surfaces.
• Lateral area is the sum of the areas of the
  lateral faces of a prism or pyramid, or the
  surface area excluding the base or bases.

3
Lateral area of a prism

• The lateral area L of a prism can be found using
  the following formula, where p is the perimeter
  of the base and h is the prism's height.
• L ph

4
Finding Lateral area

• Find the lateral area of the regular hexagonal
  prism with side lengths of 14 in. and height of
  48 in..

5
Surface area

• Surface area of a prism can be calculated by
  finding the sum of the areas of each face.
  Sometimes it is easier to find the lateral
  surface area and then add the ares of the bases.
• So, surface area of a prism is the sum of the
  lateral area and the area of the bases.
• S L 2B or
• S perimeter of base x height 2B

6
Finding surface area

• Hexagonal base can be divided into 6 congruent
  triangles( each have a height of 4 in.)

7 in.
5 in.
7
Volume of a prism

• Volume is the number of unit cubes of a given
  size that will exactly fit the interior of a
  solid.
• The volume of a prism can be found by using the
  formula V Bh ,
• Where B is the area of the base , and h is the
  height of the prism

8
Right prism

• A right prism is a prism whose lateral faces are
  all rectangles and whose lateral edges are
  perpendicular to both bases. (The height is the
  length of one edge that separates the bases)

9
Finding volume of a right prism

• Find the volume of this right prism

10
Oblique prism

• An oblique prism is a prism that has at least one
  nonrectangular face. An oblique prism is like a
  prism that has been tilted to one side.
• The formula for surface area and volume are the
  same formulas that are used for right prisms, but
  instead of using the height of a lateral edge, an
  altitude of the prism must be used.
• Remember an altitude is a segment that is
  perpendicular to, and has its endpoints on, the
  planes of the bases.

11
Finding volume
8 in.
11 in.
6 in
2 in.
12
practice

• Use the figure at the right to answer 1 and 2
• 1. Find the lateral area
• 2. Find the surface area
• 3.Find the volume of the right prism.

3 in.