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Bell WorkFind the surface area of each figure.
13 x 23 = 299 cm²
10 x 23 = 230 cm²
( ½ )(10)(12) = 60 cm²
Add them up!
SA = 299 + 299 + 230 + 60 +60
SA = 948 cm²
6 x 4 = 24 in²
3 x 4 = 12 in²
6 x 3= 18 in²
Add them up!
SA = 24 + 24 + 12 + 12+ 18 + 18
SA = 108 in²
Surface Area Continued
Definition• Surface Area – is the total number of square
units used to cover a 3-D surface.
Surface Area
• What does it mean to you?• Does it have anything to do with what is inside
of the prism?• Surface area is found by finding the area of all
the sides and then adding those answers up.• How will the answer be labeled?• Units2 because it is area!
Shortcut for surface Area
• You can find the SA of any prism by using the basic formula for SA which is:
SA= 2B + Ph• Ph = The surface area of all of the sides.– The sum of the surface areas of all of the faces
excluding the bases.• To find Ph: perimeter of the base x height of
the prism.• B = the area of the base of the prism.
Let’s start with a rectangular prism.
You can find the area for each surface and add them up, or surface area can be done using the formula.
SA = 2lw + 2lh + 2wh OR SA = 2B + Ph
Either method will give you the same answer.
Top/bottom 2(8)(4) = 64
Left/right 2(4)(7) = 56
Front/back 2(8)(7) = 112
Add them up!
SA = 232 cm²
Example:
7 cm
4 cm
8 cm
SA= 2B + Ph
B = (7)(4) = 28
P = 4 + 4 + 7 + 7 = 22
h = 8
SA= 2(28) + 22(8)
SA= 56 + 176
SA = 232 cm²
OR
Example:
8mm
9mm
6 mm 6mm
Find the AREA of each SURFACE
1. Top and bottom triangle:
A = 2(½ bh)
A =2( ½ )(6)(6)
A = 36
2. The two sides are the same.
A = 2lw
A = 2(6)(9)
A = 108
3. The back rectangle is different
A = lw
A = 8(9)
A = 72
4. ADD THEM ALL UP!
36+ 108+ 72
SA = 216 mm²
SA= 2B + Ph
SA= 2(18) + 20(9)
SA= 36 + 180
SA = 216 mm²
ORB = ( ½ )(6)(6) = 18
P = 6 + 6 + 8 = 20
h = 9
Cube
Are all the faces the same? YES
4m
How many faces are there? 6
Find the Surface area of one of the faces.
4 x 4 = 16 Take that times the number of faces.X 6
96 m2 SA for a cube.
Example
SA= 2B + Ph
SA= 2(16) + 20(15)
SA = 32 + 300
SA= 332 in²
B = 2 x 8 = 16 in²P = 2 + 2 + 8 +8 = 20 in
Find the Surface Area
Example
SA= 2B + Ph
SA= 2(184) + 50.4(21.5)
SA = 368 + 1,083.6
SA= 1,451.6 cm²
Perimeter of Base = (8.4)(6)P= 50.4 cm
Find the Surface Area
Example
CUBEArea of one face: 5² = 25
SA= (6)(25)
SA= 150 m²
Find the Surface Area
Example• The area of one base of a triangular prism is
18 square feet. The perimeter of the triangular base is 19 feet. The height of the prism is 21 feet. Find the surface area of the triangular prism.
21 ft
SA= 2B + Ph
SA= 2(18) + 19(21)
SA = 36 + 399
SA= 435 ft²
Example• How much wrapping paper do you need to
completely cover a rectangular box that is 20 inches by 18 inches by 6 inches?
SA= 2B + Ph
SA= 2(360) + 76(6)
SA= 720 + 456
SA= 1176 in²B = 20 x 18 = 360 in²
P = 20 + 20 + 18 + 18 = 76 in
Practice: Surface Area Worksheet
REMEMBER!
When in doubt….draw a net to find the surface area!