1 finding surface area step 1: flatten the 3-d figure a rectangular prism will flatten to 6...
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1
Finding Surface Area
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.
Rectangular Prism
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Finding Surface AreaStep 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
Length12
Width4
3
Finding Surface Area
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)
Rectangular Prism
Height 8
Length12
Width4
8
88
12
12
12
4
4
4
4
4
Finding Surface AreaStep 4: Find the AREA for each rectangle. (Length X Width)
Rectangular Prism
Height 8
Length12
Width 4
8
8 8
12
12
12
4
4
4
4
12 x 4
12 x 8
12 x 4
12 x 88 x 4 8 x 4
48 sq units
96 sq units
48 sq units
96 sq units32 32
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Finding Surface AreaStep 4: Find the TOTAL SURFACE AREA for the 3-D Figure
Add together the areas for each rectangle
Rectangular Prism
8
124
48 sq units
96 sq units
48 sq units
96 sq units32 32
4848
9696
3232
= 352 sq. unitsTotal surface area
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You can also use a table, instead of drawing the net.
8
12
4
Since opposite faces are congruent,you have three pairs of congruent rectangles.
Face Formula: A = bh
Area
Top 4 x 12 48
Bottom 4 x 12 48
Left 8 x 4 32
Right 8 x 4 32
Front 8 x 12 96
Back 8 x 12 96Total: 352 sq units
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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
8
CPS Practice:
The top and bottom faces each have an area of:
A) 64•224B)56C)None of the above
(Fill out a table for this figure as you do each of the next few questions.)
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The left and right faces each have an area of:
A) 64•224B)56C)None of the above
10
The front and back faces each have an area of:
A) 64•224B)56C)None of the above
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The total surface area of this rectangular prism is:
A) 765B) 896C) 344D) 688
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Cube or SquareA cube or square will flatten to 6 equal squares.
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Triangular Prism
A triangular prism will flatten to 3 rectangles and two equal triangles.
Step 1: Flatten the 3-D figure
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Triangular Prism
8
6
8
6
15
15
15
Step 2: Transfer the dimensions to the 3-D Figure
Dimensions:
Base = 8
Height of Tri. = 6
Hypotenuse = 10
Height of prism = 15
1010
15
Triangular Prism
8
6
108
10
4
15
15
15
15
15
15
15
8
6
10
Transfer dimensions to Flattened Figure
Step 3:
6
8
16
Triangular Prism
8
6
108
10
6
15
15
15
15
15
15
15
8
6
10Find the area for each rectangle and triangle
Step 4:
8
6Step 5:
Write the area inside the specific shape
A = 8 x 15
A = 10 x 15
A = 6 x 15
120
150
90
A = 6 x 8
2 24 24
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Triangular Prism
8
6
108
10
6
15
15
15
15
15
15
15
8
6
10Add all the areas for the total surface area
Step 6:
8
6
120
150
90
24 24
90
120150
2424
408 =Total surface
area
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8
6
8
6
15
15
Try using a table instead of drawing a net.
Face A = ½(bh) Area
Triangle ½ (8 x 6) 24
Triangle ½(8 x 6) 24
Rectangle 1 8 x 15 120
Rectangle 2 6 x 15 90
Rectangle 3 10 x 15 150
Total: 408 sq units
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CPS Practice
(Fill out a table for this figure as you do each of the next few questions.)
What is the area of each of the two triangles?
•48 m²A)48 m³B)96 m²C)96 m³
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The three rectangles have the following areas:
•150, 150, 150A)150, 100, 100B)150, 150, 180C)180, 180, 150
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The total surface area of this triangular prism is:
•600A)576B)480C)The same as the surface area of the moon.
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Cylinder
A Cylinder will flatten to a rectangle and two equal circles.
Step 1: Flatten the 3-D shape
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Cylinder Step 2: Transfer the dimensions to the 3-D shape
Height - 15Diameter - 8
Formulas to use: A =
15
Height
Diameter8
r = d 2
Height15
r = 4
Diameter = 8
2Π4 = 8Π
25
radius4
Step 3: Transfer dimensions to the flattened shape
8Π = 25
Length =
15
24
Cylinder Step 4: Find the area for each shape
25
15
8
15
8
4
3.14 x 4 x 4 = 50A = 50
A = 50
A = 375
25 x 15
Step 5: Add the areas for the shapes
5050
375
425 = Total surface area
25
Or, try using a table.
15
8 Face A =πr2 orA = Ch
Area
Circle π4² 50.25
Circle π4² 50.25
Rectangle 8π x 15 376.8
Total: 477.3 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.
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CPS Practice
25
5
What is the approximate area of each of the circles in this cylinder?
•About 15 sq unitsA)About 30 sq unitsB)About 100 unitsC)About 75 sq units
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25
5
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.A)Multiply the diameter of the circle by the height.B)Multiply the radius by the height.C)Multiply any two numbers that you happen to see on the diagram.
28
25
5What is the approximate area of the lateral rectangle?
•125 sq unitsA)About 750 sq unitsB)About 75 sq unitsC)About 1,200 sq units
29
25
5
The total surface area is about:
•750 sq unitsA)825 sq unitsB)900 sq unitsC)The same as a can of Spaghettio’s.
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