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

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

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

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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…

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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…

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

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

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

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

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

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

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

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

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

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

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

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

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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

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

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

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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

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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)

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

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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

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Surface Area of Triangular Prisms

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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?

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

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Unfolded net of a triangular prism

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

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

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Practice Time!

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

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

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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

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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

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

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

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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

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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

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

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

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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

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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

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

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

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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

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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

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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…

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Base Lateral height

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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…

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Lateral height Base

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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.

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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.

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

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

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

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

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