Video solutions to help Grade 7 students learn how to find the surface area of three-dimensional objects whose surface area is composed of triangles and quadrilaterals.

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Common Core For Grade 7

• Students find the surface area of three-dimensional objects whose surface area is composed of triangles and
quadrilaterals. They use polyhedron nets to understand that surface area is simply the sum of the area of the
lateral faces and the area of the base(s).

Opening Exercise: Surface Area of a Right Rectangular Prism

On the provided grid, draw a net representing the surfaces of the right rectangular prism (assume each grid line represents inch). Then find the surface area of the prism by finding the area of the net.

Discussion: Terminology

A right prism can be described as a solid with two “end” faces (called its bases) that are exact copies of each other and rectangular faces that join corresponding edges of the bases (called lateral faces).

Exercise 1

Marcus thinks that the surface area of the right triangular prism will be half that of the right rectangular prism and wants to use the modified formula SA = 1/2(2lw + 2lh + 2wh). Do you agree or disagree with Marcus? Use nets of the prisms to support your argument.

Example 1

A right triangular prism, a right rectangular prism, and a right pentagonal prism are pictured below, and all have equal heights of h.

a. Write an expression that represents the lateral area of the right triangular prism as the sum of the areas of its lateral faces.

b. Write an expression that represents the lateral area of the right rectangular prism as the sum of the areas of its lateral faces.

c. Write an expression that represents the lateral area of the right pentagonal prism as the sum of the areas of its lateral faces.

d. What value appears often in each expression and why?

e. Rewrite each expression in factored form using the distributive property and the height of each lateral face.

f. What do the parentheses in each case represent with respect to the right prisms?

g. How can we generalize the lateral area of a right prism into a formula that applies to all right prisms?

Closing

Relevant Vocabulary

There is a region B' in E' that is an exact copy of the region B. The regions B and B' are called the

1. Why are the lateral faces of right prisms always rectangular regions?

2. What is the name of the right prism whose bases are rectangles?

3. How does this definition of right prism include the interior of the prism?