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Published byLarry Fearnley Modified over 2 years ago

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**Finding Surface Area Rectangular Prism Step 1: Flatten the 3-D figure**

A rectangular prism will flatten to 6 rectangles. Depending on the dimensions of the 3-D figure, you will have different size rectangles. 1

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**Rectangular Prism Finding Surface Area**

Step 2: Transfer the dimensions to the 3-D figure Dimensions: Length – 12 (left to right) Height – 8 (top to bottom) Width – 4 (front to back) Rectangular Prism Height 8 Width 4 Length 12 2

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**Finding Surface Area Rectangular Prism**

Step 3: Transfer the dimensions from the 3-D figure to the flattened figure Dimensions: Length – 12 (the longest side) Height – 8 (top to bottom) Width – 4 (front to back) 12 4 Height 8 Width 8 4 Length 12 12 4 8 8 4 12 4 3

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**Finding Surface Area Rectangular Prism**

Step 4: Find the AREA for each rectangle. (Length X Width) Height 8 Width 4 12 Length 12 x 4 4 48 sq units 12 12 x 8 8 96 sq units 12 12 x 4 4 48 sq units 8 12 x 8 8 32 96 sq units 32 8 x 4 8 x 4 4 12 4 4

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**Add together the areas for each rectangle**

Finding Surface Area Rectangular Prism Step 4: Find the TOTAL SURFACE AREA for the 3-D Figure Add together the areas for each rectangle 8 4 12 48 48 sq units 48 96 96 96 sq units 32 32 Total surface area 48 sq units = sq. units 32 96 sq units 32 5

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**You can also use a table, instead of drawing the net.**

Since opposite faces are congruent, you have three pairs of congruent rectangles. 8 4 12 Face Formula: A = bh Area Top 4 x 12 48 Bottom Left 8 x 4 32 Right Front 8 x 12 96 Back Total: 352 sq units 6

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Group Practice: Fill out this table on your scratch paper to find the area for this figure. Face Formula: A = bh Area Top Bottom Left Right Front Back Total: _____ sq units 7

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**CPS Practice: The top and bottom faces each have an area of: A) 64 224**

56 None of the above (Fill out a table for this figure as you do each of the next few questions.) 8

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**The left and right faces each have an area of:**

224 56 None of the above 9

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**The front and back faces each have an area of:**

224 56 None of the above 10

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**The total surface area of this rectangular prism is:**

B) 896 C) 344 D) 688 11

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Cube or Square A cube or square will flatten to 6 equal squares. 12

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**Triangular Prism Step 1: Flatten the 3-D figure**

A triangular prism will flatten to 3 rectangles and two equal triangles. 13

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**Triangular Prism Step 2: Transfer the dimensions to the 3-D Figure 15**

Base = 8 Height of Tri. = 6 Hypotenuse = 10 Height of prism = 15 8 8 10 10 15 6 6 15 14

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**Triangular Prism 15 15 8 8 10 10 15 8 4 6 15 15 8 10 Step 3: 6 15**

Transfer dimensions to Flattened Figure 6 15 15

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Triangular Prism 15 15 8 8 10 10 A = 8 x 15 15 8 120 6 6 15 15 A = 10 x 15 8 Step 4: A = 6 x 8 2 10 24 24 150 Find the area for each rectangle and triangle 6 15 A = 6 x 15 90 6 Step 5: Write the area inside the specific shape 15 16

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Triangular Prism 15 15 8 8 120 10 10 15 150 8 120 90 6 6 15 24 15 24 8 Step 6: 408 =Total surface area 10 24 24 150 Add all the areas for the total surface area 6 15 90 6 15 17

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**Try using a table instead of drawing a net.**

15 8 8 15 6 6 Face A = ½(bh) Area Triangle ½ (8 x 6) 24 ½(8 x 6) Rectangle 1 8 x 15 120 Rectangle 2 6 x 15 90 Rectangle 3 10 x 15 150 Total: 408 sq units 18

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**CPS Practice What is the area of each of the two triangles? 48 m²**

(Fill out a table for this figure as you do each of the next few questions.) 19

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**The three rectangles have the following areas:**

150, 150, 150 150, 100, 100 150, 150, 180 180, 180, 150 20

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**The total surface area of this triangular prism is:**

600 576 480 The same as the surface area of the moon. 21

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**Cylinder Step 1: Flatten the 3-D shape**

A Cylinder will flatten to a rectangle and two equal circles. 22

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**Cylinder r = d 2 Step 2: Transfer the dimensions to the 3-D shape**

Diameter 8 Step 3: Transfer dimensions to the flattened shape Diameter = 8 radius Length = 4 Height 2Π4 = 8Π 8Π = 25 15 Height 15 15 Height - 15 25 Diameter - 8 Formulas to use: A = r = 4 r = d 2 23

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**Cylinder Step 4: Find the area for each shape 8 8 3.14 x 4 x 4 = 50**

25 Step 5: Add the areas for the shapes 15 25 x 15 15 A = 375 50 50 375 425 = Total surface area 4 A = 50 24

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Or, try using a table. 8 Face A =πr2 or A = Ch Area Circle π4² 50.25 Rectangle 8π x 15 376.8 15 Total: sq units Just remember that the circumference of the circle is always one side of the rectangle and the height of the cylinder is the other. 25

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CPS Practice 5 What is the approximate area of each of the circles in this cylinder? About 15 sq units About 30 sq units About 100 units About 75 sq units 25 26

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**How do you find the area of the lateral rectangle for this cylinder?**

Multiply the circumference of the circle by the height of the cylinder. Multiply the diameter of the circle by the height. Multiply the radius by the height. Multiply any two numbers that you happen to see on the diagram. 5 25 27

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**What is the approximate area of the lateral rectangle?**

125 sq units About 750 sq units About 75 sq units About 1,200 sq units 5 25 28

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**The total surface area is about:**

750 sq units 825 sq units 900 sq units The same as a can of Spaghettio’s. 5 25 29

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