Surface Area of Prisms

SECTION 5.06

After completing this lesson, you will be able to say:

I can represent three-dimensional figures using nets made of rectangles and triangles.

I can use nets to find the surface area of prisms.

I can use nets to solve real-world and mathematical problems about surface area.

Polyhedrons

What is a polyhedrons?

Polyhedrons are three-dimensional shapes because they have a length, a width, and a height.All faces of a polyhedron are polygonsAll sides of a polygon must be straight. Since there are no curved edges in a polyhedron, cylinders are not polyhedrons

Key Vocabulary

Prism:A polyhedron whose bases are congruent and sides are parallelograms.

Face:A side of a three-dimensional figure.

Bases:The top and bottom faces of a prism.

Prism

• A Prism is named by the shape of its base.

Since the base of this prism is a rectangle, we call this a Rectangular Prism

Can you name the Prism

Can you name the Prism

CubePentagonal Prism

Triangular Prism

Key Features of a Prism

Edge:The line segment where two faces of a polyhedron meet.

Vertices:Plural for vertex; the corner where two or more edges of a polyhedron meet.

Nets

The picture of the unfolded box is called a net

 To create a net, you simply unfold the faces of the polyhedron (or prism) so it lays flat.

Creating a Net

• The easiest way to calculate the surface area of a prism is to use a net• Think about what the box would look like if you cut the box open and laid it

out. Each part of the box is drawn and labeled on the graph.• Can you match each part?

Using a net to find Surface Area

• We can use the net of the rectangular prism to find the surface area.

• Drawing your net is the first step.

Using Nets to find the Surface Area

Next you want to find the area of each part:

To find the total area or Surface area, you add up the areas of the partsSA = 110 + 22 + 110 + 22 + 110 + 20 + 20 = 304 in2

Try It!

Use a net to solve for the surface area

Check your work

Surface of Triangular Prisms

Nico wants to stain his new skateboard ramp shown in the image with varnish

What is the total surface area of the prism?

Surface Area of a Triangular Prism

First, draw your net.

Now we need to find the area of each part.

Surface area of Triangular Prisms

Now that you completed this lesson, you should be able to say:

I can represent three-dimensional figures using nets made of rectangles and triangles.

I can use nets to find the surface area of prisms.

I can use nets to solve real-world and mathematical problems about surface area.