2 Surface area is how much area is on the outside of a solid 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.SquareRectangleTriangle3 units3 units3 units4 units4 unitsArea = b x h= 9 square unitsArea = b × h= 12 square unitsArea = (b × h) ÷ 2= 6 square units
4 What We Know:Surface —On a prism, surfaces refer to the flat faces that make up the solid.Rectangular prismshave 6 faces.All faces are rectangles.Triangular prismshave 5 faces.2 are triangles, 3 are rectangles
5 How do we find the surface area of a rectangular prism? 10 units12 units6 units
6 The front and back are identical. The left and right are identical. 10 units12 units6 unitsWe can “unfold” the prismto make its net.We can find the area ofeach rectangle.The front and back are identical.The left and right are identical.BACKThe top and bottom rectangles are identical6 units10 unitsBOTTOMRIGHTLEFTTop = u2Bottom = u2TOP View6 × 12 =72sq. units6 × 12 =72sq. units10 × 12 = 120square units10 × 12 = 120square units12 units12 units12 units12 unitsFront = u2Back = u2+6 units10 units6 units10 unitsLeft Side = u2Right Side = 72 u26 × 10 = 60square units6 × 10 = 60square unitsFRONT6 units10 units504u2
7 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 = u2Bottom = u210 units12 units6 unitsFront = u2Back = u2+Left Side = u2Right Side = 72 u2504u2Surface Area
8 Find the surface area of this rectangular prism. QuickCheck!Find the surface area of this rectangular prism.Click to reveal the answer.Front = 9 cm × 12 cm = 108 cm2Back = Front = 108 cm2Left Side = 9 cm × 8 cm = 72 cm2Right Side = Left Side = 72 cm2Top = 8 cm × 12 cm = 96 cm2Bottom = Top = 96 cm2Surface Area = 552 cm28 cm9 cm12 cm
9 How do think we find the surface area of a triangular prism?
10 + We can find the area of each polygon. We can “unfold” the prism 12 units10 units8 units6 unitsWe can find thearea ofeach polygon.We can “unfold”the prismto make its net.We add up theareas of all thefaces.6 units8 units(6 × 8) ÷ 2 =24 u2(6 × 8) ÷ 2 =24 u212 units10 units12 units6 units12 units10 unitsRectangle 1 = 120 u2Rectangle 2 = 72 u2Rectangle 3 = 120 u2Triangle 1 = u2Triangle 2 = u210 × 12 =120 u26 × 12 =72 u210 × 12 =120 u2+360u28 units
11 Click to reveal the answer. QuickCheck!What are the shapes and measurements for each of the faces of this triangular prism? List them.Click to reveal the answer.Rectangle 1 = 3 in × 3 inRectangle 2 = 3 in × 5 inRectangle 3 = 3 in × 4 inTriangle 1 = 3 in × 4 inTriangle 2 = 3 in × 4 in5 inches4 inches3 inches3 inches
12 Now find the surface area of this triangular prism. QuickCheck!Now find the surface area of this triangular prism.Click to reveal the answer.Rectangle 1 = 3 in × 3 in = 9 in2Rectangle 2 = 3 in × 5 in = 15 in2Rectangle 3 = 3 in × 4 in = 12 in2Triangle 1 = (3 in × 4 in) ÷ 2 = 6 in2Triangle 2 = (3 in × 4 in) ÷ 2 = 6 in2Total Surface Area = 48 in25 inches4 inches3 inches3 inches
13 End of Surface Area Lesson. Continue with Volume
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 = 25 square units Cubes in Bottom Layer × Height 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.To determine the number of cubes that fill this rectangular prism, first we will find out how many cubes will fit in the bottom.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.If we know how many SQUARES are on the bottom then we could set a cube on each of those squares.Volume of Rectangular Prisms5 unitsLENGTH × WIDTH5 units × 5 units = 25 square units25 squares 25 cubes!Cubes in Bottom Layer × Height25 cubes × 5= 125 cubes5 units
17 V = L × W × H V = B.A. x H The formula: Volume of rectangular prism = Base Area × HeightV = B.A. x HB.A. = AREA of the Base H = Height or distance between the basesThe Base Area (B.A.) for any rectangular prism isLength × Widthso we can also state the formula for a rectangular prism as:V = L × W × H5 units5 units × 5 units × 5 units = 125 cubic units
18 Let’s find the volume of this rectangular prism by using the formula B.A. × HV = B.A. × HV = (5 × 4) × 20V = 20 × 20V = 400 cm320 cm4 cm5 cmRemember that our units will alwaysbe in terms of “cubic” units
19 Volume of Rectangular Prism = B.A. x H Click to reveal the answer. QuickCheck!A packing box is 20 cm high, 15 cm wide and 18 cm deep. Find the volume.Volume of Rectangular Prism = B.A. x HVolume = (15 x 18) x 20Volume = 270 x 20Volume = 5400 cm3Click to reveal the answer.
20 V = B.A. x H 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 HB.A. = AREA of the Base H = Height or distance between the basesB.A. = 12 units2 (the number of cubes in one layer)V = B. A. x HV = 12 units2 × 5 unitsV = 60 units3Then we can multiply that by the height, which is the number of layers.4 units6 unitsFirst find the area of the base, which is a triangle:B.A. = (B x H) ÷ 2B.A. = (6 × 4) ÷ 2B.A. = 12 units2The area of the base tells us how many cubes are in one layer.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)andmultiply by the height (the distance between the bases)
22 V = B.A. x H Let’s find the volume of this triangular prism V = Area of the Base × HeightV = (16 cm × 10 cm ÷ 2) × 15 cmV = (80 cm2) × 15 cmV = 1200 cm310 cm15 cm16 cmRemember that our units will alwaysbe in terms of “cubic” unitsContinue
23 Find the volume of this triangular prism. QuickCheck!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?Click to reveal the answer.Volume = B.A. × HVolume = (6 ft × 5 ft ÷ 2) × 8 ftVolume = 120 ft36 ft5 ft8 ft