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Surface Area of a Rectangular Prism Getting Ready – Calling Stick Activity What is the name of shape D? A? B? C? Square A B C D Rectangle Cube Rectangular Prism Getting Ready – Think – Pair – Share What similarities and differences do you see between any of these shapes? Square A B Cube C D Rectangle Rectangular Prism Calculating Surface Area A rectangular prism always has 6 sides, or faces. ____ Top Side 2 Back Front Bottom Length (L) Side 1 Height (H) Width (W) Extension Calculating Surface Area To help us see all six faces of a rectangular prism, mathematicians sometimes unfold the box to see a drawing called a net. Internet Applet Vocabulary Net of a cube Net Back to lesson Faces Vocabulary When a box is unfolded so you can see all the sides as a flat pattern, this is called it’s net. Net of a Rectangular Prism Rectangular Prism Back to lesson Back Vocabulary Each side of a rectangular prism is called a face. A rectangular prism has six faces. Back to lesson Back Example So, how do we find the surface area of this rectangular prism? 2 Front = 4 cm x 3 cm = 12 cm Back Side 2 2 Back 4 = 4 cm x 3 cm = 12 cm 2 Top 2 4 Side 1 = 2 cm x 3 cm = 6 cm2 3 Front 3Side 3 cm Side 2 = 2 cm x 3 cm = 6 cm2 Top = 4 cm x 2 cm = 8 cm2 2 cm 4 cm Bottom = 4 cm x 2 cm = 8 cm2 + Bottom Scaffolding 52 cm2 Internet Applet Answer Find the surface area Calculate the area of your rectangular prism Summary Question – Think – Pair – Share Find the mistake(s) in the problem below. 6 2 4 Top Front = 6 in x 12 in = 72 in 4 6 Back = 6 in x 12 in = 72 in2 Side 22 = 4 cm x 12 cm = 48 in 12 in Side = 4 in x 6 in = 24 in 22 = 4 cm x 12 cm = 48 in Side = 4 in x 6 in 24 in 12 Front 12 2 = 24 in Top = 6 in x 4 in 4 in Bottom = 6 in x 4 in = 24 in2 + 22 6 in 240 in The side is not 4 x 6, = 288 in it’s 4 x 12!! Scaffolding Warm Up OBJECTIVE: SWBAT find the surface area of a rectangular prism 1. Find the area of the front, side, and top of this rectangular prism. 4 Front = 3 in x 12 in = 36 in2 12 12 Top 4 3 Front 3 inSide 12 in Side = 3 in x 4 in = 12 in2 3 Top 4 in = 4 in x 12 in = 48 in2 2) Find the circumference and area of a circle with radius 5 cm. Radius = 5 cm C = 2πr = 2 x 3.14 x 5 cm = 31.4 cm A = πr2 = 3.14 x 5 cm x 5 cm = 78.5 cm2 Scaffolding Summarize – Whole Class Discussion OBJECTIVE: SWBAT find the surface area of a rectangular prism 1. Find the area of the front, side, and top of this rectangular prism. Top Front 3 inSide 12 in 4 in Front Side Top+ = 36 in2 = 12 in2 = 48 in2 96 in2 Surface Area = 96 in2 …right? Summarize – Whole Class Discussion OBJECTIVE: SWBAT find the surface area of a rectangular prism No! 1. Find the area of the front, side, and top of this rectangular prism. Remember, there are six No! No! 2 Front = 36 in sides to a rectangular No! 2No! Side = 12 in prism… No! Top No! + =and 48 Back in2 • Front Top Front Side • Side 1 and Side 2 No! 2 No! 3 in 96 in No! No! • Top and Bottom 12 in No! 4 in Surface Area = 96 in2 …right? Summarize – Whole Class Discussion OBJECTIVE: SWBAT find the surface area of a rectangular prism 1. Find the area of the front, side, and top of this rectangular prism. Top Front 3 inSide 12 in 4 in Front = 36 in2 Back = 36 in2 Side = 12 in2 Side = 12 in2 Top = 48 in2 Bottom = 48 in2 96 in2 + 96 in2 Surface Area = 192 in2 Agenda: OBJECTIVE: SWBAT find the surface area of a rectangular prism 1) 2) 3) 4) 5) 6) 7) Warm Up – Individual Work Launch – Whole class discussion Explore: Making the Equation for Surface Area – Partner Activity Class work Review Class work Summary Exit Ticket – Individual Work to be handed in to teacher Launch – Whole Class Discussion A formula uses only letters, numbers, and symbols to find a mathematical value. You already know area formulas for some shapes: Width (W) Rectangle Are youLength ready for (L) some algebra?! Triangle Height (h) Area = LxW Area = ½bxh Area = 3.14 x r x r = πr2 base (b) Circle radius (r) Explore With your partner, try to write a formula to find the surface area using l for length, w for width, and h for height. Length (l) Width (w) Top Width (w) Length (l) Back Side 2 Side 1 Height (h) Height (h) Front Height (h) Bottom Width (w) Length (l) Don’t forget that there are six sides on a rectangular prism! Need a hint? Write the formulas for the front, side 1, and the top. Then write the formulas for the back, side 2, and the bottom. Scaffolding Formula for Surface Area – Whole Class SA =2 LH + 2 WH + 2 LW Area of the Front = Length x Height Area of the Back = Length x Height Area of Side 1 = Width x Height Area of Side 2 = Width x Height Area of Top = Length x Width Area of Bottom = Length x Width Width Scaffolding Length Top Width Back Length Height (h) Side 2 Side 1 Height Front Height Bottom Width (w) Length (l) One cool thing about this equation is that it doesn’t matter in what order you find the area of the faces. SA = 2 LH WH+ +2 LW ++ 22LW LH 2 WH This is an example of the Commutative Property of Addition ( a + b = b + a ) Practice Find area of this rectangular prism: Let’sthe trysurface an example… 3 SA = 2LH + 2WH + 2LW 6 Top 4Front 6 6 cm 3 4 4 cm Side 3 cm 2 = 48 cm 2 x 6 cm x 4 cm + 2 = 24 cm 2 x 3 cm x 4 cm + 2 = 36 cm 2 x 3 cm x 6 cm 108 cm2 Scaffolding Class Work Take a shot at solving some of the problems on the class work. I’ll time you! Class work #1 SA = 2(L x H) + 2(W x H) + 2(L x W) SA = 2( 8 x 5 ) + 2( 4 x 5 ) + 2( 8 x 4 ) SA = 2 (40 cm2) + 2( 20 cm2) + 2( 32 cm2) SA = 80 cm2 + 40 cm2 + 64 cm2 SA = 184 cm2 Back to Solutions Class work #2 SA = 2(L x H) + 2(W x H) + 2(L x W) SA = 2( 12 x 4 ) + 2( 3 x 4 ) + 2( 12 x 3 ) SA = 2 (48 in2) + 2( 12 in2) + 2( 36 in2) SA = 96 in2 + 24 in2 + 72 in2 SA = 192 in2 Back to Solutions Exit Ticket On a separate piece of notebook paper to be handed in to your teacher: Choose one of the following and answer on your paper: 1. Explain how to find surface area. 2. Find the surface area of this 5 rectangular prism. 2 2 5 4 cm 3. If you aren’t sure about #1 or #2, 4 4 what is confusing to you about 2 cm surface area? 5 cm Scaffolding Prism Surface Area Formula Top : lw Bottom : lw Front : hl Back : hl Left : hw Right : hw : lw + lw + hl + Total hl + hw + hw : 2lw + 2hl + 2hw : 2(lw + hl + hw) Surface Area of a Prism 21st Century Lessons Surface Area of a Rectangular Prism Lesson Thanks to Sarita Thomas Shane Ulrich