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Surface area is how much area is on the outside of a solid. We measure surface area with square units.

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What We Know: AREA is the amount of space inside a flat surface, which is measured with square units. 3 units Area = b x h = 9 square units 4 units 3 units Area = b × h = 12 square units 4 units 3 units Area = (b × h) ÷ 2 = 6 square units SquareRectangle Triangle

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What We Know: Surface —On a prism, surfaces refer to the flat faces that make up the solid. Rectangular prisms have 6 faces. All faces are rectangles. Triangular prisms have 5 faces. 2 are triangles, 3 are rectangles

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How do we find the surface area of a rectangular prism? 10 units 12 units 6 units

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10 units 12 units 6 units 10 units 12 units 6 units 10 units 12 units 6 units 10 units TOP View 10 × 12 = 120 square units 10 × 12 = 120 square units BOTTOM Top = 120 u2u2 Bottom = 120 u2u2 Front = 60 u 2 Back = 60 u 2 Left Side = 72 u 2 Right Side = 72 u 2 504 u2u2 FRONT BACK 6 × 10 = 60 square units 6 × 10 = 60 square units LEFT 6 × 12 = 72 sq. units 6 × 12 = 72 sq. units RIGHT We can “unfold” the prism to make its net. We can find the area of each rectangle. The top and bottom rectangles are identical The front and back are identical. The left and right are identical. +

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To find the surface area of a rectangular prism, you are finding the area of each of the 6 rectangular surfaces and adding them up to get a total. Top = 120 u2u2 Bottom = 120 u2u2 Front = 60 u 2 Back = 60 u 2 Left Side = 72 u 2 Right Side = 72 u 2 504 u2u2 Surface Area +

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Find the surface area of this rectangular prism. 12 cm 8 cm 9 cm Front = 9 cm × 12 cm = 108 cm 2 Back = Front = 108 cm 2 Left Side = 9 cm × 8 cm = 72 cm 2 Right Side = Left Side = 72 cm 2 Top = 8 cm × 12 cm = 96 cm 2 Bottom = Top = 96 cm 2 Surface Area = 552 cm 2 Click to reveal the answer.

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How do think we find the surface area of a triangular prism?

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12 units 10 units 8 units 6 units 10 units 12 units 6 units 12 units 10 units 12 units 10 units 6 units 8 units We can “unfold” the prism to make its net. We can find the area of each polygon. 10 × 12 = 120 u 2 6 × 12 = 72 u 2 10 × 12 = 120 u 2 (6 × 8) ÷ 2 = 24 u 2 (6 × 8) ÷ 2 = 24 u 2 Rectangle 1 = 120 u2u2 Rectangle 2 = 72 u2u2 Rectangle 3 = 120 u2u2 Triangle 1 = 24 u2u2 Triangle 2 = 24 u2u2 360 u2u2 We add up the areas of all the faces. +

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What are the shapes and measurements for each of the faces of this triangular prism? List them. 3 inches 4 inches 5 inches Rectangle 1 = 3 in × 3 in Rectangle 2 = 3 in × 5 in Rectangle 3 = 3 in × 4 in Triangle 1 = 3 in × 4 in Triangle 2 = 3 in × 4 in Click to reveal the answer.

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Now find the surface area of this triangular prism. 3 inches 4 inches 5 inches Rectangle 1 = 3 in × 3 in = 9 in 2 Rectangle 2 = 3 in × 5 in = 15 in 2 Rectangle 3 = 3 in × 4 in = 12 in 2 Triangle 1 = (3 in × 4 in) ÷ 2 = 6 in 2 Triangle 2 = (3 in × 4 in) ÷ 2 = 6 in 2 Total Surface Area = 48 in 2 Click to reveal the answer.

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End of Surface Area Lesson. Continue with Volume

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OLUME

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What We Need to Understand Volume is the amount of space inside a three- dimensional object. In order to measure volume, we need a three- dimensional unit, so we use cubes. The size of the cube depends on the unit that the object is measured with, so we can measure with cubic inches, cubic feet, cubic centimeters, etc. A cubic inch is a cube that measures an inch on each of its side; a cubic mile is a cube that measures a mile on each of its sides. (That’s BIG!)

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To determine the number of cubes that fill this rectangular prism, first we will find out how many cubes will fit in the bottom. If we know how many SQUARES are on the bottom then we could set a cube on each of those squares. The number of SQUARES that will fill the bottom (base) is the same as the AREA of the base. Since the bottom is a rectangle, we can use LENGTH × WIDTH to determine the number of squares on the base. 5 units LENGTH × WIDTH 5 units × 5 units = 25 square units 25 squares 25 cubes! Now we can determine how many LAYERS of these cubes there are in the prism. The number of layers is the same as the prism’s HEIGHT. 5 units Cubes in Bottom Layer × Height 25 cubes × 5 = 125 cubes Volume of Rectangular Prisms

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The formula: 5 units × 5 units × 5 units = 125 cubic units 5 units Volume of rectangular prism = Base Area × Height V = B.A. x H B.A. = AREA of the Base H = Height or distance between the bases The Base Area (B.A.) for any rectangular prism is Length × Width so we can also state the formula for a rectangular prism as: V = L × W × H

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4 cm 5 cm 20 cm Let’s find the volume of this rectangular prism by using the formula B.A. × H V = B.A. × H V = (5 × 4) × 20 V = 20 × 20 V = 400 cm 3 Remember that our units will always be in terms of “cubic” units

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Volume of Rectangular Prism = B.A. x H Volume = (15 x 18) x 20 Volume = 270 x 20 Volume = 5400 cm 3 Click to reveal the answer. A packing box is 20 cm high, 15 cm wide and 18 cm deep. Find the volume.

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Volume of Triangular Prisms The formula for finding the volume of a triangular prism is the same as our formula for a rectangular prism: V = B.A. x H B.A. = AREA of the Base H = Height or distance between the bases First find the area of the base, which is a triangle: B.A. = (B x H) ÷ 2 B.A. = (6 × 4) ÷ 2 B.A. = 12 units 2 4 units 6 units The area of the base tells us how many cubes are in one layer. 5 units B.A. = 12 units 2 (the number of cubes in one layer) V = B. A. x H V = 12 units 2 × 5 units V = 60 units 3 Then we can multiply that by the height, which is the number of layers.

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CAUTION!! Don’t be fooled by a triangular prism that is not sitting on its base! We still need to find the area of the base (the triangle) and multiply by the height (the distance between the bases)

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16 cm 15 cm Continue Let’s find the volume of this triangular prism V = B.A. x H V = Area of the Base × Height V = (16 cm × 10 cm ÷ 2) × 15 cm V = (80 cm 2 ) × 15 cm V = 1200 cm 3 Remember that our units will always be in terms of “cubic” units 10 cm

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Find the volume of this triangular prism. Volume = B.A. × H Volume = (6 ft × 5 ft ÷ 2) × 8 ft Volume = 120 ft 3 Click to reveal the answer. Mark’s scout group has a pup tent that is the shape of a triangular prism. It is 8 feet long, 6 feet wide and has a height of 5 feet from the ground to the peak of the roof. How many cubic feet of air are inside the tent? 8 ft 6 ft 5 ft

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THE END

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