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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 = SA = 948 cm² 6 x 4 = 24 in² 3 x 4 = 12 in² 6 x 3= 18 in² Add them up! SA = SA = 108 in²

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**Surface Area Continued**

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

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**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!

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**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.

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**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.

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**OR Example: SA= 2B + Ph B = (7)(4) = 28 P = 4 + 4 + 7 + 7 = 22 h = 8**

7 cm 4 cm 8 cm SA= 2B + Ph B = (7)(4) = 28 P = = 22 h = 8 SA= 2(28) + 22(8) SA= SA = 232 cm² Top/bottom 2(8)(4) = 64 Left/right 2(4)(7) = 56 Front/back 2(8)(7) = 112 Add them up! SA = 232 cm² OR

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**3. The back rectangle is different**

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 mm 3. The back rectangle is different A = lw A = 8(9) A = 72 4. ADD THEM ALL UP! SA = 216 mm² SA= 2B + Ph SA= 2(18) + 20(9) SA= SA = 216 mm² B = ( ½ )(6)(6) = 18 P = = 20 h = 9 OR

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**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.

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**Example Find the Surface Area SA= 2B + Ph SA= 2(16) + 20(15)**

SA= 332 in² B = 2 x 8 = 16 in² P = = 20 in

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**Example Find the Surface Area SA= 2B + Ph SA= 2(184) + 50.4(21.5)**

SA= 1,451.6 cm² Perimeter of Base = (8.4)(6) P= 50.4 cm

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**Example Find the Surface Area CUBE Area of one face: 5² = 25**

SA= (6)(25) SA= 150 m²

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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 = SA= 435 ft² 21 ft

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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= SA= 1176 in² B = 20 x 18 = 360 in² P = = 76 in

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**Practice: Surface Area Worksheet REMEMBER. When in doubt…**

Practice: Surface Area Worksheet REMEMBER! When in doubt….draw a net to find the surface area!

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