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Math Help - Surface Area of Pyramid

  1. #1
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    Surface Area of Pyramid

    Hey ALL - I'm working on this and could really use some help. Am I even going in the right direction here? Please see Attached for Diagram:

    Bottom Pyramid – Apothem is half of the height = 6cm
    LA = Lateral Area = ph
    P = 4s
    P=4(10)=40
    LA = 40(12) = 480
    Slant Height = √180
    LA = 1/2pL
    LA = ½(40)( √180) = 268.33
    SA = 268.33 + B
    B = 102 = 100
    SA = 368.33cm2
    Top Pyramid
    Pythagorean Theorem to find 3rd side
    9 + 16 = C2
    C = 5cm
    P = 4(5cm) = 20cm
    LA = 20(10) = 200
    LA = ½(20)( √180) = 134.16
    SA = 134.16 + B
    B = 52 = 25
    SA = 159.16cm2

    Add Both Surface Areas = 368.33 + 159.16 = 527.49cm2
    Attached Thumbnails Attached Thumbnails Surface Area of Pyramid-pyramid.jpg  
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  2. #2
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    Re: Surface Area of Pyramid

    Trapezoid upper face 3,4,5 rt triangle
    lower face 6,8,10 rt tri
    Draw a face of pyramid from base to vertex
    Area of face = 1/2 slant height * base
    Repeat for each face
    How does the area of pyramid face compare to the trapezoid face area
    Calculate the total trap.face area and add the upper trap face
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  3. #3
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    Re: Surface Area of Pyramid

    Quote Originally Posted by SmokeDawg View Post
    Hey ALL - I'm working on this and could really use some help. Am I even going in the right direction here? Please see Attached for Diagram:

    Bottom Pyramid – Apothem is half of the height = 6cm
    LA = Lateral Area = ph
    P = 4s
    P=4(10)=40
    LA = 40(12) = 480
    Slant Height = √180
    LA = 1/2pL
    LA = ½(40)( √180) = 268.33
    SA = 268.33 + B
    B = 102 = 100
    SA = 368.33cm2
    Top Pyramid
    Pythagorean Theorem to find 3rd side
    9 + 16 = C2
    C = 5cm
    P = 4(5cm) = 20cm
    LA = 20(10) = 200
    LA = ½(20)( √180) = 134.16
    SA = 134.16 + B
    B = 52 = 25
    SA = 159.16cm2

    Add Both Surface Areas = 368.33 + 159.16 = 527.49cm2
    Maybe I don't understand your question correctly but ...:

    The top area is a right triangle whose right angle's legs have the lengthes 3 and 4 respectively. So it's area is 6 cm².

    The base area is a right triangle whose right angle's legs have the lengthes 6 and 8 respectively. So it's area is 24 cm².

    Since the height of the trapezoidal faces is 12 the area of each trapezoidal face is calculated by: A = (1/2)(a + c) * h
    where a and c are the lengthes of the parallels. The total area of the three trapezoidal faces is calculated by: (15/2 + 12/2 + 9/2)*12

    I've got a total surface area of 246 cm²
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  4. #4
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    Re: Surface Area of Pyramid

    By the way why don't you use the answer here: Surface Area of Pyramid
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  5. #5
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    Re: Surface Area of Pyramid

    The model will not require the area of base
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