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Math Help - slant height/total area/volume problem. did i do this one right?

  1. #1
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    Post slant height/total area/volume problem. did i do this one right?

    IS this correct. Im not so sure, especailly about c. Thanks.

    A pyramid has a square base of side 10. A lateral edge of the pyramid is 13.

    a) Find the slant height.
    12, because of specail right triangle 5,12,13

    b)Find the total area.
    LA= 1/2pl
    LA= 1/2 40x12
    LA=240
    TA=LA+B
    TA=240+100
    TA= 340units^3

    c) Find the volume.
    V=1/3Bh
    V=1/3x100xh
    (height h=2leg30 (12=slant edge)
    12=2leg30
    6=leg30
    6=apothem
    6^2+hieght^2=12^2
    36+ h^2=144
    h^2=108
    h=6squarerootof3)
    V=1/3x100x6(sr3) (sr= square root)
    V=100/3 x 6(sr3)
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  2. #2
    Member Ranger SVO's Avatar
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    Someone will correct me if I'm wrong, but I think c is wrong.

    It should be 400 units^3

    (1/3) * (area of the base) * ( height)
    (1/3) * 100 * 12 = 400 units cubed
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  3. #3
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    that is wrong 12 is not the hieght. it is the slant height
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  4. #4
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    Quote Originally Posted by sarahgasoline View Post

    b)Find the total area.
    LA= 1/2pl
    LA= 1/2 40x12
    LA=240
    TA=LA+B
    TA=240+100
    TA= 340units^3
    The area of base is (10)(10)=100
    The area of each triangle is (1/2)(10)(12)=60
    In total we have,
    100+4(60)=100+240=340
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  5. #5
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    thats what i have! my main question was is c correct?
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  6. #6
    Member Ranger SVO's Avatar
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    I told you I would get corrected if I was wrong.

    The height of the pyrimide is sqrt(119)

    So we have (1/3) * 100 * height
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  7. #7
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    how did you get sqrt of 119? i got sqrt of 108
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  8. #8
    Member Ranger SVO's Avatar
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    Hope this explination makes sense, it makes sense to me
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  9. #9
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    i did that. and got sqrt108
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  10. #10
    Member Ranger SVO's Avatar
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    s = 12 so s^2=144
    You said the side of the base is 10

    so r = (1/2) of 10 so r = 5 then r^2=25

    144 - 25 = 119
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  11. #11
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    yeah but your not using the base you have to use the apothem to find the hieght
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  12. #12
    Member Ranger SVO's Avatar
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    Isn't the apothem of a regular polygon the shortest distance between the center of the polygon and the side of the polygon.

    Please correct me if I am wrong but the apothem of a square is half the length of the side.

    In my previous diagram r is the apothum

    I get the apothem is equal to 5 units
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