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heather040200

  • 3 years ago

HELP! PIC BELOS I GIVE MEDALS:) the lateral area of the right regular triangular prism is 18pi cm^2. find the total surface area. give your answer in decimal form rounded of to 2 decimal places

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  1. heather040200
    • 3 years ago
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  2. mathstudent55
    • 3 years ago
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    The lateral area of the prism is the sum of the areas of the three rectangles whose dimensions are 3 and x.

  3. mathstudent55
    • 3 years ago
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    Each rectangular face has an area of 3x, so all three faces have a combined area of 3 * 3x = 9x. The lateral area = 9x = 18pi

  4. mathstudent55
    • 3 years ago
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    9x = 18pi x = 2pi

  5. mathstudent55
    • 3 years ago
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    Now we need the area of the bases.

  6. mathstudent55
    • 3 years ago
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    Each base is a regular triangle with side = 2pi

  7. mathstudent55
    • 3 years ago
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    |dw:1365464719385:dw|

  8. mathstudent55
    • 3 years ago
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    Each base of the prism is a regular (equilateral) triangle with side length of 2pi. If you drop an altitude, as the picture above shows, you create two 30-60-90 triangles. The ratio of the lengths of the legs of a 30-60-90 triangle is 1 : sqrt(3) Since the short leg measures pi, the long leg measures pi * sqrt(3) The long leg is the altitude of the large triangle, whose base measure 2pi

  9. mathstudent55
    • 3 years ago
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    The area of a triangle is A = (1/2)bh Here we have A = (1/2)(2pi)(pi * sqrt(3) ) = pi^2*sqrt(3) Since there are two bases, the area of the 2 bases is 2*pi^2*sqrt(3)

  10. mathstudent55
    • 3 years ago
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    Since the lateral area is 18pi, the total surface area is SA = (18pi + 2*pi^2*sqrt(3) ) cm^2 Now you can calculate an approximate value with your calculator.

  11. heather040200
    • 3 years ago
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    72.21

  12. mathstudent55
    • 3 years ago
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    I get 90.67

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