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Bell Work Find 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.

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bell work find the surface area of each figure
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

definition
Definition
  • Surface Area – is the total number of square units used to cover a 3-D surface.
surface area
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
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.
slide6

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 + 2whORSA = 2B + Ph

Either method will give you the same answer.

slide7

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

Top/bottom 2(8)(4) = 64

Left/right 2(4)(7) = 56

Front/back2(8)(7) = 112

Add them up!

SA = 232 cm²

OR

slide8

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

Example:

8mm

9mm

6 mm 6mm

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

B = ( ½ )(6)(6) = 18

P = 6 + 6 + 8 = 20

h = 9

OR

slide9
Cube

Are all the faces the same?

YES

How many faces are there?

6

4m

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
Example

Find the Surface Area

SA= 2B + Ph

SA= 2(16) + 20(15)

SA = 32 + 300

SA= 332 in²

B = 2 x 8 = 16 in²

P = 2 + 2 + 8 +8 = 20 in

example1
Example

Find the Surface Area

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

example2
Example

Find the Surface Area

CUBE

Area of one face: 5² = 25

SA= (6)(25)

SA= 150 m²

example3
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.

SA= 2B + Ph

SA= 2(18) + 19(21)

SA = 36 + 399

SA= 435 ft²

21 ft

example4
Example
  • How much wrapping paper do you need to completely cover a rectangular box that is 20 inches by 18 inches by 6inches?
  • SA= 2B + Ph
  • SA=2(360) + 76(6)
  • SA= 720 + 456
  • SA= 1176 in²

B = 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
Practice: Surface Area WorksheetREMEMBER!When in doubt….draw a net to find the surface area!
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