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heather040200
 2 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
heather040200
 2 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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mathstudent55
 2 years ago
Best ResponseYou've already chosen the best response.1The lateral area of the prism is the sum of the areas of the three rectangles whose dimensions are 3 and x.

mathstudent55
 2 years ago
Best ResponseYou've already chosen the best response.1Each rectangular face has an area of 3x, so all three faces have a combined area of 3 * 3x = 9x. The lateral area = 9x = 18pi

mathstudent55
 2 years ago
Best ResponseYou've already chosen the best response.19x = 18pi x = 2pi

mathstudent55
 2 years ago
Best ResponseYou've already chosen the best response.1Now we need the area of the bases.

mathstudent55
 2 years ago
Best ResponseYou've already chosen the best response.1Each base is a regular triangle with side = 2pi

mathstudent55
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1365464719385:dw

mathstudent55
 2 years ago
Best ResponseYou've already chosen the best response.1Each 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 306090 triangles. The ratio of the lengths of the legs of a 306090 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

mathstudent55
 2 years ago
Best ResponseYou've already chosen the best response.1The 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)

mathstudent55
 2 years ago
Best ResponseYou've already chosen the best response.1Since 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.
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