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Surface Area of a Rectangular Prism

Surface Area of a Rectangular Prism. Activating background knowledge:. A. C. What is the name of shape C?. What is the name of shape D?. What is the name of shape A?. What is the name of shape B?. B. Square. Cube. D. Rectangle. Rectangular Prism.

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Surface Area of a Rectangular Prism

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  1. Surface Area of a Rectangular Prism

  2. Activating background knowledge: A C What is the name of shape C? What is the name of shape D? What is the name of shape A? What is the name of shape B? B Square Cube D Rectangle Rectangular Prism

  3. Getting Ready – Think – Pair – Share C What similarities and differences do you see between any of these shapes? A B Square Cube D Rectangular Prism Rectangle

  4. Calculating Surface Area Top Back Side 2 Side 1 Front Bottom A rectangular prism always has faces. 6 Height (H) Width (W) Length (L) Extension

  5. Calculating Surface Area To help us see all six faces of a rectangular prism, we can unfold the box to see a drawing called a net. Internet Applet Vocabulary Net of a cube Net Faces Back to lesson

  6. Vocabulary When a box is unfolded so you can see all the sides as a flat pattern, this is called it’s net. Rectangular Prism Net of a Rectangular Prism Back to lesson Back

  7. Vocabulary Each side of a rectangular prism is called a face. A rectangular prismhas six faces. Back to lesson Back

  8. 3 cm 2 cm 4 cm + Example So, how do we find the surface area of this rectangular prism? Back Side 2 = 4 cm x 3 cm = 12 cm2 Front 4 2 = 4 cm x 3 cm = 12 cm2 2 Back 4 Top Side 1 = 2 cm x 3 cm = 6 cm2 3 3 Front Side = 2 cm x 3 cm = 6 cm2 Side 2 Top = 4 cm x 2 cm = 8 cm2 Bottom = 4 cm x 2 cm = 8 cm2 Bottom 52 cm2 Internet Applet Scaffolding Answer

  9. To find the surface area: Calculate the area of all the faces of your prism and add them together.

  10. Summary Question – Think – Pair – Share Side + Find the mistake(s) in the problem below. 6 Top Front 4 = 6 cmx 12 cm = 72 cm2 4 6 = 6 cmx 12 cm = 72 cm2 Back Front 12 cm = 4 cm x 12 cm= 48 cm2 = 4 cm x 12 cm= 48 cm2 Side = 4 cm x 6 cm = 24 cm2 Side = 4 in x 6 cm = 24 cm2 12 12 Top = 6 cmx 4 cm = 24 cm2 Bottom 4 cm = 6 cmx 4 cm = 24 cm2 240 cm2 6 cm = 288 cm2 The side is not 4 x 6, it’s 4 x 12!! Scaffolding

  11. Warm Up Radius = 5 cm OBJECTIVE: SWBAT find the surface area of a rectangular prism 1. Find the area of the front, side, and top of this rectangular prism. = 36 cm2 = 3 cm x 12 cm Front 4 12 Side = 3 cm x 4 cm = 12 cm2 Top 12 4 3 3 Front Side Top = 4 cm x 12 cm = 48 cm2 3 cm 12 cm 4 cm 2) Find the circumference and area of a circle with 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

  12. 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 = 36 cm2 Front Side Side = 12 cm2 3 cm 12 cm = 48 cm2 Top 4 cm + 96 cm2 Surface Area = 96 cm2 …right?

  13. Summarize – Whole Class Discussion + No! No! No! OBJECTIVE: SWBAT find the surface area of a rectangular prism No! No! No! No! 1. Find the area of the front, side, and top of this rectangular prism. No! Top Front = 36 cm2 No! No! Side = 12 cm2 Front No! 3 in Side • Remember, there are six sides to a rectangular prism… • Front and Back • Side 1 and Side 2 • Top and Bottom 12 in = 48 cm2 Top 4 in No! 96 cm2 Surface Area = 96 cm2 …right?

  14. = 36 cm2 Back = 12 in2 Side = 48 cm2 Bottom + 96 cm2 96 cm2 Summarize – 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 = 36 cm2 Front = 12 cm2 Side Front 3 cm Side 12 cm = 48 cm2 Top 4 cm Surface Area = 192 cm2

  15. Formula for calculating surface area of – prisms: Rectangle Width (W) Length (L) Triangle Height (h) base (b) Circle radius (r) A formula uses only letters, numbers, and symbols to find a mathematical value. You already know area formulas for some shapes: Are you ready for some algebra?! L x W Area = Area = ½ b x h 3.14 x r x r = πr2 Area =

  16. 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. Top Side 1 Front Height (h) Length (l) Width (w) Width (w) Length (l) Width (w) Length (l) Height (h) Height (h) Don’t forget that thereare six sides on arectangular prism! Back 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. Side 2 Bottom Scaffolding

  17. Formula for Surface Area – Whole Class SA = 2 LH + WH 2 + LW 2 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 Length Width Width Top Back Side 2 Side 1 Length Front Height (h) Height Height Bottom Width (w) Length (l) Scaffolding

  18. One cool thing about this equation is that it doesn’t matter in what order you find the area of the faces. SA = 2 WH +2 LW + 2 LH SA = 2 LH + 2 WH + 2 LW This is an example of the Commutative Property of Addition ( a + b = b + a )

  19. Find the surface area of this rectangular prism: 4 cm 3 cm 6 cm Practice Let’s try an example… SA = 2LH + 2WH + 2LW 6 3 Top 3 2 x 6 cm x 4 cm = 48 cm2 Front 6 Side 4 + 4 2 x 3 cm x 4 cm = 24 cm2 + 2 x 3 cm x 6 cm = 36 cm2 108 cm2 Scaffolding

  20. Class Work Take a shot at solving some of the problems on the class work. I’ll time you!

  21. Class work #1 Calculate the SA SA = 2(L x H) + 2(W x H) + 2(L x W) SA = 2( x ) + 2( x ) + 2( x ) SA = 2 ( cm2) + 2( cm2) + 2( cm2) SA = cm2+ cm2+ cm2 SA = cm2 Back to Solutions

  22. Class work #1 Solution 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

  23. Class work #2 Calculate the SA cm cm cm SA = 2(L x H) + 2(W x H) + 2(L x W) SA = 2( x ) + 2( x ) + 2( x ) SA = 2( cm2) + 2( cm2) + 2( cm2) SA = cm2+ cm2+ cm2 SA = cm2 Back to Solutions

  24. Class work #2 cm cm cm 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

  25. Check if you have been successful In your workbook : Choose one of the following and answer on your paper: 1. Explain how to find surface area. 2. Find the surface area of thisrectangular prism. 3. If you aren’t sure about #1 or #2,what is confusing to you aboutsurface area? 5 2 2 5 4 cm 4 4 2 cm 5 cm Scaffolding

  26. Surface Area of a Prism

  27. 21st Century Lessons Surface Area of a Rectangular Prism Lesson Thanks to Sarita Thomas Shane Ulrich

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