Geometric Nets

Nets and Surface Area

6.G.A.1

Objective

• Recognize that surfaces of some three-dimensional (3-D) shapes are composed of two-dimensional (2-D) faces or polygons

• Use a net to represent a 3-D figure (polyhedron)

• Use a net to determine the surface area of a polyhedron made up of rectangles and triangles

Vocabulary

• Polyhedron: a closed, 3-D shape with flat sides.

• Base: the face of a geometric figure from which the height can be measured, refer to a face of a polyhedron.

• face: each flat side of a polyhedron

• net: a flat "unfolded" representation of a prism or pyramid

• surface area: the sum of all areas of the faces of a figure

• prism: type of polyhedron that has two bases that are identical copies of each other.

• pyramid: type of polyhedron whose one base is a polygon and whose other faces are triangles.

• triangular pyramid: a 3-D figure that has two parallel triangular faces that are the same size and shape

First Let's Review

What do we remember about area?

Multiple Choice

Area is...

• the space inside of an object

• the space around an object

Multiple Choice

What is the formula for the area of a parallelogram?

• $$A=\frac{bh}{2}$$

• $$A=bh$$

• $$A=\frac{1}{2}bh$$

Multiple Select

What is the formula for the area of a triangle? select all that apply

• $$A=\frac{bh}{2}$$  
  

• $$A=bh$$  
  

• $$A=\frac{1}{2}bh$$  
  

• $$A=\frac{b}{h}$$   

Fill in the Blank

Find the area. Write the number only.

Fill in the Blank

Find the area. Write the number only

Multiple Choice

Which number is NOT needed to solve the problem?

• 10 in

• 8 in

• 1 ft

• all numbers are needed

Fill in the Blank

Find the area. Write the number only

Fill in the Blank

If we are going to fold the net how many faces does the polyhedron have?

Different polyhedra and their nets

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Multiple Choice

What 3D solid does this net create?

• Rectangular Prism

• Rectangular Pyramid

• Cube

• Square Prism

Multiple Choice

What do you call the flat surface of a 3-Dimensional figure?

• Pyramid

• Prism

• Net

• Area

Multiple Choice

Which of the following is a cube?

Multiple Choice

Which of the following is a pyramid?

Multiple Choice

Which of the following is true to a pyramid?

• It has one base and all faces are equal faces

• It has one base and all faces are triangle

• All bases are triangle and one face

Multiple Choice

Which figure will this net make?

• Rectangular Prism 

• Triangular Prism

• Triangular Pyramid 

• Cube

Multiple Choice

In a rectangular prism, how many faces are there?

• 5

• 4

• 3

• 6

Multiple Choice

Which figure will this net make?

• Cone

• Triangular Prism

• Square Pyramid 

• Cube

Multiple Choice

Which figure will this net make?

• Triangular Pyramid

• Hexagonal Pyramid

• Octagonal Pyramid 

• Cube

Multiple Choice

Which of the following cannot be folded into CUBE?

Multiple Choice

What is the name of the 3-D figure shown?

• rectangular pyramid

• square pyramid

• rectangular prism

• square prism

Multiple Choice

If you fold the given net into 3-D figure, what will be the result?

• cube

• rectangular prism

• rectangular pyramid

• rectangular net

Multiple Choice

Find the Surface area of a triangular prism.

• 1248 cm²

• 704 cm²

• 624 cm²

• 512 cm²

Multiple Choice

What is the surface area of the cube?

• 12 cm²

• 36 cm²

• 24 cm²

• 64 cm²

Multiple Choice

The side length of a cube is 3 in. What is true about the surface area of the cube?

• 1. The cube has 4 surfaces that each have an area of 6 square units, so the total surface area is 24 square units.

  
  

• The cube has 6 surfaces that each have an area of 6 square units, so the total surface area is 36 square units

• The cube has 4 surfaces that each have an area of 9 square units, so the total surface area is 36 square units.

• The cube has 6 surfaces that each have an area of 9 square units, so the total surface area is 54 square units.

Fill in the Blank

The net for a rectangular prism has three pairs of rectangles: 3 units by 8 units, 2  units by 6 units, 2 units by 4  units. What is the surface area, in square units, for this prism?

Multiple Choice

Vignesh is calculating the surface area of the prism whose net is given.

He performs the following steps:
1. There are two faces that each have an area of 6×4=24  square units.
2. There are two faces that each have an area of 6×6=36  square units.

3.There are two faces that each have an area of 3×4=12  square units.

4. The total surface area of the prism is 108  square units.

In which step did Vignesh first make a mistake?

• Step 1

• Step 2

• Step 3

• Step 4