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Area vs Surface Area
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Surface Area Surface Area is the sum of the area of all of the faces of a 3-dinemtional figure. We often use nets to help us determine surface area. 2-D (flat) figures have area 3-D figures have surface area
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Surface Area vs. Area State whether each of the following shapes will have area or surface area.
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Surface Area vs. Area State whether each of the following situations will involve area or surface area. I want to wrap the new PS3 that I bought as a gift. (Hint: it is in the box still) I just bought property and I want to measure how much land I own. I am painting a shed and I need to know how much paint to buy. I am painting one wall of my house and I need to know how much paint to buy. Surface Area Area Surface Area Area
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Finding Surface Area We can calculate surface area in two ways:
Substitute into a formula. Draw a net and find the area of each section. *If you do not know the formula, the second option will always work!
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Surface Area Using a Net
Use your knowledge of area to calculate the surface area of the rectangular prism. Draw a net first to help you. 4cm 3 cm 7 cm
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Surface Area Length = 7 cm Width = 3 cm Height = 4 cm Add!
SA = 122 cm2 3 cm Top= 21 cm2 7 cm Back = 28 cm2 4 cm 7 cm 3 cm 3 cm Bottom= 21 cm2 Base = 12 cm2 3 cm Base = 12 cm2 4 cm 4 cm 4 cm Front= 28 cm2 7 cm
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Surface Area All four triangles are the same: A = ½ bh
A = ½ (3)(4) = 6 cm2 Area of the base (square) A = LW or A=s2 A = 32 = 9 cm2 Total Surface Area = 4 triangles + 1 square = 4(6 cm2 ) + 9 cm2 = 33 cm2 4 cm 3 cm
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Surface Area using a Formula
Surface area of a Rectangular Prism SA = 2LW + 2LH + 2HW SA = 2(7)(3) + 2(7)(4) + 2(3)(4) SA = 122 cm2 Length = 7 cm Width = 3 cm Height = 4 cm
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Common Surface Area Formulas
Rectangular Prism SA = 2LW + 2LH + 2WH Square Pyramid SA = 2bh + b2 Cube SA = 6s2
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Activity Using the object you brought in and a ruler, determine how much paper would be needed to wrap the outside of your object. Hint: This means we need to find the surface area. You can do this using a formula or by drawing a net.
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