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InsanityxP

  • 2 years ago

What is the surface area of the composite figure? ~Attachment in comments~

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  1. InsanityxP
    • 2 years ago
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  2. Shane_B
    • 2 years ago
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    Take it in pieces and sum up the values at the end. It's going to be:\[SA_{bottom}+4SA_{side}+4SA_{triangle~side}\]

  3. Shane_B
    • 2 years ago
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    If you're stumped on this let me know and I'll walk you through it.

  4. InsanityxP
    • 2 years ago
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    It would help if you could walk me through it, please?

  5. Shane_B
    • 2 years ago
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    Ok, the bottom of the figure is a square with 6mm sides right? Well, the SA of a square is just side*side: \[6mm*6mm=36mm^2\]

  6. Shane_B
    • 2 years ago
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    The sides are rectangles so it's basically SA = LW:\[7mm*6mm=42mm^2\]

  7. Shane_B
    • 2 years ago
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    The top parts are just triangles with a 6mm base and a height of 4mm. The SA of a triangle is (1/2)bh:\[\frac{(6mm)(4mm)}{2}=12mm^2\]

  8. Shane_B
    • 2 years ago
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    Now use the first equation I posted which sums it all up to get the total surface area. If you work it out I'll double-check your answer.

  9. InsanityxP
    • 2 years ago
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    For some reason I've got 90 mm^2 but that's not even close to one of the answers I have :/

  10. Shane_B
    • 2 years ago
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    I think I lost you...here:\[SA_{total}=SA_{bottom}+4SA_{side}+4SA_{triangle~side}\]\[SA_{total}=36+4(42)+4(12)=?\]

  11. Shane_B
    • 2 years ago
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    There's no magic formula when doing these types of problems. You just take the individual areas and sum them up at the end.

  12. InsanityxP
    • 2 years ago
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    252 mm^2?

  13. Shane_B
    • 2 years ago
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    Yes

  14. InsanityxP
    • 2 years ago
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    Thank you!

  15. Shane_B
    • 2 years ago
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    yw, good luck :)

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