Surface Area

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$Math and Chemistry - McGraw-Hill Ryerson$

Reflect on Your Findings5. a) How did you use the area of each face to calculate the totalamount of material used to make your cardboard box?b) Can you think of a shorter way to find the total area withouthaving to find the area of each face? Explain your method.Example 1: Calculate the Surface Area of a Right Rectangular Prisma) Draw the net of this right rectangular prism.b) What is the area of each face?c) What is the surface area of the prism?Solutiona)4 cm10 cm6 cm6 cm10 cm4 cmsurface area• the number of squareunits needed to covera 3-D object• the sum of the areas ofall the faces of anobjectb) The right rectangular prism has faces that are three different sizes.6 cmfront or back10 cmA = l × wA = 10 × 6A = 60The area of the frontor back is 60 cm 2 .4 cmtop or bottom10 cmA = l × wA = 10 × 4A = 40The area of the topor bottom is 40 cm 2 .4 cmends6 cmA = l × wA = 6 × 4A = 24The area of eachend is 24 cm 2 .Area is measured insquare units.For example, squarecentimetres, squaremetres, etc.c) The total surface area is the sum of the areas of all the faces.The front and backhave the same area:A = 60 × 2A = 120The top and bottomhave the same area:A = 40 × 2A = 80The two ends havethe same area:A = 24 × 2A = 48Total surface area = (area of front and back) + (area of top and bottom)+ (area of ends)= 120 + 80 + 48= 248The surface area of the right rectangular prismis 248 cm 2 .You could add the areas you calculatedfirst. 60 + 40 + 24 = 124Each area is the same as the area of one otherface, so you could then multiply the total bytwo. 124 × 2 = 2485.3 Surface Area of a Prism • MHR 19
What is the surface area of this rightrectangular prism?16 cm8 cm3 cmExample 2: Calculate the Surface Area of a Right TriangularPrisma) Draw the net of this right triangular prism.b) What is the area of each face?c) What is the total surface area?Solution9 m2.6 ma)3 mStrategiesDraw a DiagramRefer to page xxx.3 m2.6 m9 mLiteracyLinkAn equilateraltriangle has threeequal sides and threeequal angles. Equalsides are shown ondiagrams by placingtick marks on them.b) The bases of the prism are equilateral triangles.The sides of the prism are rectangles.3 mrectangletriangle9 m 3 m2.6 mA = l × w A = (b × h) ÷ 2A = 9 × 3 A = (3 × 2.6) ÷ 2A = 27 A = 7.8 ÷ 2A = 3.9The area of oneThe area of onerectangle is 27 m 2 . triangle is 3.9 m 2 .20 MHR • Chapter 5
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Page 6 and 7: 4. Using isometric dot paper, draw
Page 8 and 9: Example 3: Predict and Draw the Top
Page 10: For help with #5, refer to Example
Page 13 and 14: Example 2: Build a Three-Dimensiona
Page 15 and 16: 4. Draw the net for each object. La
Page 17: Surface Area of a PrismFocus on…A
Page 21 and 22: For help with #3 and #4, refer to E
Page 23 and 24: Surface Area of a CylinderFocus on
Page 25 and 26: StrategiesDraw a DiagramRefer to pa
Page 27 and 28: • The surface area of a cylinder
Page 29 and 30: Key WordsUnscramble the letters for
Page 31 and 32: Short AnswerFor #1 to #5, choose th
Page 33 and 34: Let’s Face It!1. Play Let’s Fac

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