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Image Source: http://www.ppfl.orgTotal Surface Area is important for Painters,so that they know how much paint will be required for a job.Engineers, Designers, Scientists, Builders, Concreters,Carpet Layers, and others also use Total Surface Areasas part of their work.
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A 3D Rectangular Prismcan be unfolded to createa flat 2D shape, called the“Net” of the Prism.
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The “Total Surface Area” or“TSA” of the Prism is theArea of all of the six facesadded together.Each of the Faces is a L x WRectangle.8 cm4 cm
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The “Total Surface Area” =2 x ( 8 x 5) : Two Blues+ 2 x ( 8 x 4) : Two Yellows+ 2 x ( 4 x 5) : Two Reds= 2x40 + 2x32 + 2x20= 184 cm28 cm4 cm8 x 5 8 x 54 x 54 x 58 x 4 8 x 4
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The “Total Surface Area” =2 x ( L x W ) : Two Blues+ 2 x ( L x H ) : Two Yellows+ 2 x ( W x H ) : Two RedsLHL x W L x WW x HW x HL x H L x HTSA = 2 x(L x W) + 2x(L x H) + 2x(W x H)
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TSA = 2 x ( x ) + 2 x ( x ) + 2 x ( x )TSA = + +TSA =TSA = 2 x(L x W) + 2x(L x H) + 2x(W x H)6 m3 mWe can do the TSA of aRectangular Prism withoutdrawing out the flat 2D net.All we do is apply the Formula.
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TSA = 2 x ( 6 x 4 ) + 2 x ( 6 x 3 ) + 2 x ( 4 x 3 )TSA = 48 + 36 + 24TSA = 108 m2 ( Note that units are AREA m2 and Not VOLUME m3 )6 m3 mTSA = 2 x(L x W) + 2x(L x H) + 2x(W x H)We can do the TSA of aRectangular Prism withoutdrawing out the flat 2D net.All we do is apply the Formula.
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The Toblerone chocolate bar packaging is aclassic example of a Triangular Prism.Image Source: http://www.blogspot.com
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A 3D Triangular Prismcan be unfolded to createa flat 2D shape, called the“Net” of the Prism.The Net has two trianglesplus three rectangles.
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The “Total Surface Area” =2 x ( 6 x 5) /2 : Two Reds+ 2 x ( 8 x 7) : Two Yellows+ 1 x ( 8 x 6) : One Green= 2x15 + 2x56 + 1x48= 190 mm26 mm5 mm8 x 7( 6 x 5) /28 x 6 8 x 7( 6 x 5) /2
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The “Total Surface Area” =2 x ( b x h) /2 : Two Reds+ 2 x ( D x n) : Two Yellows+ 1 x ( D x b) : One GreenBase bHeight hD x n( b x h) /2D x b D x n( b x h) /2TSA = 2 x (b x h)/2 + 2 x (D x n) + (D x b)Only Works for Isosceles Triangle Ended PrismsOnly Works for Isosceles Triangle Ends
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For Triangular Prisms, the bestgeneral approach is to drawa “Net” of the Prism.From the Net we can work outthe Area of the Triangular Ends,and the three rectangles, andthen add them all up.We could work out that the above Prism’s Formula as :TSA = 2 x (b x h )/2 + (D x b) + (D x m) + (D x n)But it is probably easier to use a Net and the General Formula:TSA = 2 x Triangle End + Bottom Rectangle + Left Rectangle + Right Rectangle.
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If we only have the edge measurements, then we need to cutthe end Triangle in half, and apply Pythagoras Theorem towork out the Missing Height of the Prism.4 cm? cm ? cm8 cm
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A 3D Cylinder can be unwrapped to create a flat 2Dshape, called the “Net” of the Cylinder.The Net has two Circles plus one Rectangle.
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W = 10 mH = 10 mTSA = 2 x Circles + RectangleTSA =TSA = m2R = 2L =
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TSA = 2 x Circles + RectangleTSA = 2 x ∏ x 2 x 2 + 2x ∏ x 2 x 10TSA = 151 m2W = 102∏RL = 2∏ x 2Rectangle = L x WRectangle = 2x ∏ x 2 x 10Circle = ∏ x 2 x 2H = 10 mR = 2
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TSA = 2 x Circles + RectangleTSA = 2 x ∏ x R x R + 2x ∏ x R x HHL = 2∏RRectangle = L x WRectangle = 2x ∏ x R x HCircle = ∏ x R x RHTSA = 2∏R2 + 2 ∏RHR
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TSA = 2 x ∏ x R x R + 2 x ∏ x R x HTSA = 2 x 3.1416 x 3 x 3 + 2 x 3.1416 x 3 x 8TSA = 207.3 m2H = 8 mTSA = 2∏R2 + 2 ∏RHR = 3 mWe can do the TSA of aCylinder without having todraw out the flat 2D net.All we do is apply the TSA Formula.
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A 3D Square Pyramid can be unwrapped to createa flat 2D shape, called the “Net” of the Pyramid.The Net has one Square and Four Triangles.
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The “Total Surface Area” =4 x ( 8 x 10) /2 : Four Green Triangles+ 1 x ( 8 x 8) : One Blue Purple Square= 4x40 + 1x64 = 224 m28 x 8
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