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SURFACE AREA

SURFACE AREA. Surface area is how much area is on the outside of a solid. We measure surface area with square units. What We Know:. AREA is the amount of space inside a flat surface, which is measured with square units. Square. Rectangle. Triangle. 3 units. 3 units. 4 units.

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SURFACE AREA

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  1. SURFACE AREA

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

  3. What We Know: AREA is the amount of space inside a flat surface, which is measured with square units. Square Rectangle Triangle 3 units 3 units 4 units 4 units 3 units Area = s2 = 9 square units Area = l × w = 12 square units Area = ½ b × h = 6 square units

  4. 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

  5. 10 units 12 units 6 units How do we find the surface area of arectangular prism?

  6. 10 units 12 units 6 units We can “unfold” the prism to make its net. We can find the area of each rectangle. The front and backare identical. The left andright are identical. BACK The top and bottomrectangles are identical 6 units 10 units BOTTOM RIGHT LEFT Top = 120 u2 Bottom = 120 u2 TOP View 6 × 12 = 72 sq. units 6 × 12 = 72 sq. units 10 × 12 = 120 square units 10 × 12 = 120 square units 12 units 12 units 12 units 12 units Front = 60 u2 Back = 60 u2 6 units 6 units 10 units 10 units Left Side = 72 u2 Right Side = 72 u2 FRONT 6 × 10 = 60 square units 6 × 10 = 60 square units 6 units 10 units u2 504

  7. 10 units 12 units 6 units 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 u2 Bottom = 120 u2 Front = 60 u2 Back = 60 u2 Left Side = 72 u2 Right Side = 72 u2 u2 504 Surface Area

  8. Quick Check! Find the surface area of this rectangular prism. Front = 9 cm × 12 cm = 108 cm2 Back = Front = 108 cm2 Left Side = 9 cm × 8 cm = 72 cm2 Right Side = Left Side = 72 cm2 Top = 8 cm × 12 cm = 96 cm2 Bottom = Top = 96 cm2 Surface Area = 552 cm2 Click to reveal the answer. 8 cm 9 cm 12 cm

  9. How do think we find the surface area of atriangular prism?

  10. 10 units 10 units 8 units 8 units 12 units 6 units 6 units 12 units 12 units 12 units 6 units 10 units 10 units 8 units We can find the area of each polygon. We can “unfold” the prism to make its net. We add up the areas of all the faces. ½ × 6 × 8 = 24 u2 ½ × 6 × 8 = 24 u2 10 × 12 = 120 u2 6 × 12 = 72 u2 10 × 12 = 120 u2 Rectangle 1 = 120 u2 Rectangle 2 = 72 u2 Rectangle 3 = 120 u2 Triangle 1 = 24 u2 Triangle 2 = 24 u2 u2 360

  11. Quick Check! What are the shapes and measurements for each of the faces of this triangular prism? List them. 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. 5 inches 4 inches 3 inches 3 inches

  12. Quick Check! Now find the surface area of this triangular prism. Rectangle 1 = 3 in × 3 in = 9 in2 Rectangle 2 = 3 in × 5 in = 15 in2 Rectangle 3 = 3 in × 4 in = 12 in2 Triangle 1 = 3 in × 4 in = 6 in2 Triangle 2 = 3 in × 4 in = 6 in2 Total Surface Area = 48 in2 Click to reveal the answer. 5 inches 4 inches 3 inches 3 inches

  13. End of Surface Area Lesson. Continue with Volume

  14. OLUME

  15. 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!)

  16. 5 units 5 units To determine the number of cubesthat fill this rectangular prism, firstwe will find out how many cubeswill fit in the bottom. If we know how many SQUARESare 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. Now we can determine how manyLAYERS of these cubes there are inthe prism. The number of layers is the same as the prism’s HEIGHT. Volume of Rectangular Prisms 5 units LENGTH × WIDTH 5 units × 5 units = 25 square units 25 squares  25 cubes! Cubes in Bottom Layer × Height 25 cubes × 5 = 125 cubes

  17. 5 units 5 units 5 units The formula: Volume of rectangular prism = AREA of the Base × height V = Bh B = AREA of the Baseh = height or distance between the bases The area of the base (B) for any rectangular prism is length × width, so we can also state the formula for a rectangular prism as: V = l × w × h 5 units × 5 units × 5 units = 125 cubic units

  18. Let’s find the volume of this rectangular prism by using the formula l × w × h V = l × w × h V = 5 cm × 4 cm × 20 cm V = (5 × 4 × 20) cm3 V = 400 cm3 20 cm 4 cm 5 cm Remember that our units will always be in terms of “cubic” units

  19. Quick Check! A packing box is 20 cm high, 15 cm wide and 18 cm deep. Find the volume. Volume of Rectangular Prism = l × w × h Volume = 20 cm × 15 cm × 18 cm Volume = 5400 cm3 Click to reveal the answer.

  20. 6 units 4 units Volume of Triangular Prisms The formula for finding the volume of a triangular prism is the same as our first formula for a rectangular prism: V = Bh B = AREA of the baseh = height or distance between the bases The area of the base tells us how many cubes are in one layer. B = 12 units2(the number of cubes in one layer) V = Bh V = 12 units2 × 5 units V = 60 units3 Then we can multiply that by the height, which is the number of layers. First find the area of the base, which is a triangle: B = ½ bh B = ½ × 6 × 4 B = 12 units2 5 units

  21. 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)

  22. Let’s find the volume of this triangular prism V = Bh V = Area of the base × height V = (½ × 16 in × 10 in) × 15 in V = (80 in2) × 15 in V = 1200 in3 10 in 15 in 16 in Remember that our units will always be in terms of “cubic” units Continue

  23. Quick Check! Find the volume of this triangular prism. 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? Volume = B × h Volume = ½ (6 ft × 5 ft) × 8 ft Volume = 120 ft3 Click to reveal the answer. 5 ft 8 ft 6 ft

  24. End of lesson

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