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Ms. Julien East Cobb Middle School (Adapted from Mr. Tauke’s PPT)

Application: How much cardboard does it take to make a cardboard box? The manufacturers have to know this in order to make the boxes.

When wrapping gifts, you are covering the outside of the box. This is another example of surface area of a rectangular prism.

Consider what you learned about areas and nets: So… how do you think you could get the surface area of a rectangular prism? Put on your thinking caps and brainstorm for a moment…

Looking at the net, you see that TO FIND THE SURFACE AREA OF A RECTANGULAR PRISM, YOU NEED TO FIND THE AREA OF ALL 6 FACES. Let’s explore this idea…

Do you see the RED (front) face? What are the dimensions of this rectangle? 10 in. 4 in.

Do you see another face that is just like the RED (front) face? Where is it located? Keep an eye on the next screen!

Yes, it’s on the back. 10 in. 4 in. 10 in. 4 in. FRONTBACK

Now there are 2 rectangles 40 in 2 that each have an area of 40 sq. in.

Do you see the BLUE (side) face? What are the dimensions of this rectangle? 4 in. 7 in.

Do you see another face that is just like the BLUE face? Where is it located?

Yes, it’s on the left side. 4 in. 7 in. 4 in. SIDE 1SIDE 2

Now there are 2 rectangles that each have an area of 28 sq. in. 28 in 2

Do you see the GREEN (top) face? What are the dimensions of this rectangle? 10 in. 7 in.

Do you see another face that is just like the GREEN face? Where is it located?

Yes, it’s on the bottom. 10 in. 7 in. 10 in. 7 in. BOTTOMTOP

Now there are 2 rectangles that each have an area of 70 sq. in. 70 in 2

Now we just need to add all the areas of the sides together. + + + + 70 in 2 28 in 2 40 in 2 28 in 2 70 in 2

The total Surface Area for this rectangular prism is 40 + 40 + 28 + 28 + 70 + 70 = 276 in 2

2(lw) + 2(wh) + 2(lh) 2(40) + 2(28) + 2(70) 80 + 56 + 140 276 in 2

Use the formula: 2(lw) + 2(wh) + 2(lh) 2(34) + 2(412) + 2(312) 2(12) + 2(48) + 2(36) 24 + 96 + 72 192 cm 2

What is special about a cube? It has 6 square faces! Using the example to the left, what is the area of 1 face? 5 5 = 25 ft 2 Since there are 6 equal faces, what is the surface area? 6 25 = 150 ft 2 So, for SA of a cube, find the area of one face and then multiply by 6. What do you think the formula is? Yea, good job!! SA Cube = 6s 2 (s = length of one side)

What is the area of this cube, if its height is 8 in.? 6 8282 6 64 384 in 2

SA Rect. Prism = 2(lw) + 2(wh) + 2(lh) SA Cube = 6s 2 1) What is the surface area of a pizza box that has a length of 10 in, a width of 12 in, and a height of 2 in? 2)How much wrapping paper is needed to cover a box that is 7 cm long, 8 cm wide, and 3 cm tall? 3)What is the surface area of a Rubik’s Cube that is 3 inches tall? 4)Which has more surface area, a cube that is 10 in wide, or a rectangular prism that is 12 in wide, 10 in long, and 8 in tall? 1) 328 in2 2) 202 cm2 3) 54 in2 4) cube = 600in2, rect. prism = 592in2

Surface Area of Triangular Prisms

Definition: The sum of the areas of all of the faces of a three-dimensional figure. Ex. How much construction paper will I need to fit on the outside of the shape?

A triangular prism has 5 faces. FRONT BACK RIGHT LEFT BOTTOM 2 Triangular bases 3 rectangular sides

Unfolded net of a triangular prism

A triangular prism has 5 faces. FRONT BACK RIGHT LEFT BOTTOM

In order to find the surface area, find the area of each face. Then add all of the areas. FRONT BACK RIGHT LEFT BOTTOM

Practice Time!

1) Find the surface area of the triangular prism. 10 ft 20 ft 8 ft 5 ft

1) Find the surface area of the triangular prism. 10 ft 20 ft 10 ft 8 ft 20 ft 5 ft

1) Find the surface area of the triangular prism. 10 ft 20 ft 10 ft 8 ft 20 ft 5 ft 40 sq ft 100 sq ft 200 sq ft

40 + 40 + 100 + 100 + 200 = 480 sq ft 10 ft 20 ft 10 ft 8 ft 20 ft 5 ft 40 sq ft 100 sq ft 200 sq ft

2) Find the surface area of the triangular prism. 12 ft 16 ft 5 ft 8 ft

2) Find the surface area of the triangular prism. 12 ft 16 ft 12 ft 5 ft 16 ft 8 ft

2) Find the surface area of the triangular prism. 12 ft 16 ft 12 ft 5 ft 16 ft 8 ft 30 sq ft 128 sq ft 192 sq ft

30 + 30 + 128 + 128 + 192 = 508 sq ft 12 ft 16 ft 12 ft 5 ft 16 ft 8 ft 30 sq ft 128 sq ft 192 sq ft

3) Find the surface area of the triangular prism. 15 ft 22 ft 8 ft 10 ft

3) Find the surface area of the triangular prism. 15 ft 22 ft 15 ft 8 ft 22 ft 10 ft

3) Find the surface area of the triangular prism. 15 ft 22 ft 15 ft 8 ft 22 ft 10 ft 60 sq ft 220 sq ft 330 sq ft

60 + 60 + 220 + 220 + 330 = 890 sq ft 15 ft 22 ft 15 ft 8 ft 22 ft 10 ft 60 sq ft 220 sq ft 330 sq ft

4) Find the surface area of the triangular prism. 2.5 ft 8 ft 2 ft 4 ft

4) Find the surface area of the triangular prism. 2.5 ft 8 ft 2.5 ft 2 ft 8 ft 4 ft

4) Find the surface area of the triangular prism. 2.5 ft 8 ft 2.5 ft 2 ft 8 ft 4 ft 2.5 sq ft 32 sq ft 20 sq ft

2.5 + 2.5 + 32 + 32 + 20 = 89 sq ft 2.5 ft 8 ft 2.5 ft 2 ft 8 ft 4 ft 2.5 sq ft 32 sq ft 20 sq ft

Consider what you learned previously about finding surface area of a rectangular prisms and triangular prisms: So… how do you think you could get the surface area of a square pyramids? Put on your thinking caps and brainstorm for a moment…

Base Lateral height

Consider what you learned previously about surface area of a rectangular pyramids: So… how do you think you could get the surface area of a triangular pyramids? Put on your thinking caps and brainstorm for a moment…

Lateral height Base

A pyramid is a polyhedron in which the base is a polygon and the lateral faces are triangles with a common vertex. The intersection of two lateral faces is a lateral edge. The intersection of the base and a lateral face is a base edge. The altitude or height of a pyramid is the perpendicular distance between the base and the vertex.

More on pyramids A regular pyramid has a regular polygon for a base and its height meets the base at its center. A pyramid is a solid with a polygonal base formed by connecting each point of the base to a single given point (apex) that is above or below the flat surface containing the base. Each triangle is a lateral face of a pyramid.

a. Examine the pyramid below. If surface area measures the total area of all of the faces, find the surface area of the pyramid.

Rectangle (8)(8) + 4 (½(8)(5)) 64 + 4(20) 64 + 80 144 in 2 + 4 triangles

7.12 – SURFACE AREA Use the new formula to find the surface area of each shape.

Now, begin your homework. Be sure to use the correct formulas and SHOW ALL YOUR WORK!

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