9.1 Surface Area of Prisms Lessons 1 & 2

9.1 Surface Area of Prisms Lesson 1

Objectives:

• Students will be able to use two-dimensional nets to represent three-dimensional figures.

• Students will be able to find surface areas of rectangular and triangular prisms and cubes.

• NC.7.G.6 Solve real-world and mathematical problems involving: 

  Area and perimeter of two-dimensional objects composed of triangles, quadrilaterals, and polygons. Volume and surface area of pyramids, prisms, or three-dimensional objects composed of cubes, pyramids, and right prisms.

What is a prism?

A prism is a 3-D figure that has two congruent and parallel faces that are polygons. The remaining faces are parallelograms.

A prism always has two bases. These bases are congruent...

...if you find the area of one base, you will know the area of the other base.

Prisms also have faces...

Sometimes called lateral faces, these are all of the other sides of the prism.

Each face of a prism may have different dimensions, so pay attention to the measurements!

Nets

2-D shape representing a 3-D figure.

Composite figures - made up of multiple 2-D shapes

*Nets can be folded to make the 3-D figure that they represent.

We can draw nets to help us find the surface area of a prism.

Surface Area?

• the area of each surface, or shape, making up the figure

We will focus only on these three types of prisms...

Rectangular Prism

Triangular Prism

Cube

Steps for Finding the Surface Area of a Prism

Steps

• identify the shapes on each side - draw them out if you need to!

• identify the formulas needed for each shape

• find the area of each side

• add the areas of each side together

Rectangular Prisms

https://youtu.be/7L4H9HwcAOg

Rectangular Prism

• Find your length, width, and height

• You should have 3 numbers

• Write each number

Rectangular Prism

• Find your length, width, and height

• write each at the end of the Y

Rectangular Prism

• find your length, width, and height

• write each at the end of the Y

• multiply each number by the number next to it

Rectangular Prism

• find your length, width, and height

• write each at the end of the Y

• multiply each number by the number next to it

Rectangular Prism

• find your length, width, and height

• write each at the end of the Y

• multiply each number by the number next to it - write the answers in the middle

Rectangular Prism

• find your length, width, and height

• write each at the end of the Y

• multiply each number by the number next to it - write the answers in the middle

Rectangular Prism

• find your length, width, and height

• write each at the end of the Y

• multiply each number by the number next to it - write the answers in the middle

• double every product -- why? because opposite sides (faces and bases) are congruent!

Rectangular Prism

• find your length, width, and height

• write each at the end of the Y

• multiply each number by the number next to it - write the answers in the middle

• double every product -- why? because opposite sides (faces and bases) are congruent!

• add the areas together

Rectangular Prism

• find your length, width, and height

• write each at the end of the Y

• multiply each number by the number next to it - write the answers in the middle

• double every product -- why? because opposite sides (faces and bases) are congruent!

• add the areas together

Let's Practice!

Multiple Choice

Find the surface area of the rectangular prism.

• 36 ft²

• 72 ft²

• 11 ft²

Multiple Choice

Find the surface area of the rectangular prism.

• 10,800 in²

• 3,600 in²

• 3,060 in²

Multiple Choice

Find the surface area of the rectangular prism.

• 468 cm²

• 396 cm²

• 648 cm²

Triangular Prisms

https://youtu.be/HtXPpqKud5U

Triangular Prism

• Find the base and height of the triangular bases

Triangular Prism

• Find the base and height of the triangular bases

•  $\frac{b\ \times\ h}{2}$  
  

Triangular Prism

• Find the base and height of the triangular bases

•  $\frac{b\ \times\ h}{2}$  
  

• Remember, the bases are congruent!

Triangular Prism

• Find the base and height of the triangular bases

•  $\frac{b\ \times\ h}{2}$  
  

• Remember, the bases are congruent!

• Find the area of each rectangular face:  $A\ =\ length\ \times\ width$  

Triangular Prism

• Find the base and height of the triangular bases

•  $\frac{b\ \times\ h}{2}$  
  

• Remember, the bases are congruent!

• Find the area of each rectangular face:  $A\ =\ length\ \times\ width$  

Triangular Prism

• Find the base and height of the triangular bases

•  $\frac{b\ \times\ h}{2}$  
  

• Remember, the bases are congruent!

• Find the area of each rectangular face:  $A\ =\ length\ \times\ width$  

Triangular Prism

• Find the base and height of the triangular bases

•  $\frac{b\ \times\ h}{2}$  
  

• Remember, the bases are congruent!

• Find the area of each rectangular face:  $A\ =\ length\ \times\ width$  

• Find the sum (add) all of the areas

Triangular Prism

• Find the base and height of the triangular bases

•  $\frac{b\ \times\ h}{2}$  
  

• Remember, the bases are congruent!

• Find the area of each rectangular face:  $A\ =\ length\ \times\ width$  

• Find the sum (add) all of the areas

Let's Practice!

Multiple Choice

• 180 in²

• 3,120 in²

• 224 in²

Multiple Choice

• 768 in²

• 30,420 in²

• 822 in²

Multiple Choice

• 492 cm²

• 624 cm²

• 672 cm²

Multiple Choice

• 60 cm²

• 94 cm²

• 78 cm²

Cube

https://youtu.be/NPFSV6nEK_Q

Cube

• there are two ways that we can find the surface area of a cube...

Cube

• there are two ways that we can find the surface area of a cube...

• Remember, each face has the same dimensions!

Cube

• Remember, each face has the same dimensions!

•  $A\ =\ l\ \times w$  

Cube

• Remember, each face has the same dimensions!

•  $A\ =\ l\ \times\ w$  

• Each of the 6 faces has the same area..

• ... multiply the area by 6

Cube

• Remember, each face has the same dimensions!

•  $A\ =\ l\ \times\ w$  

• Each of the 6 faces has the same area..

• ... multiply the area by 6

• OR

• use the formula:  $A\ =\ 6\ s^2$  

• s = the length of one side

Let's Practice!

Multiple Choice

Find the surface area of the cube.

• 24 in²

• 12 in²

• 20 in²

Multiple Choice

Find the surface area of the cube.

• 36 in²

• 27 in²

• 54 in²

Multiple Choice

Find the surface area of the cube.

• 300 cm²

• 600 cm²

• 500 cm²

Multiple Choice

Find the surface area of the rectangular prism.

• 358 cm²

• 420 cm²

• 348 cm²