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Find the lateral area of a right triangular prism with an equilateralbase length of 5cm and height of 10cm.

  • geometry -

    Area = 3 equal rectangles + 2 equal equilateral triangles
    the rectangels are easy, each is 5 by 10 or 50 cm^2

    For the triangle, if you know two sides and the contained angle Ø between those sides, then the area
    = (1/2)(side1)(side2)sinØ
    we know it is equilateral so the angle is 60°
    area of base triangle = (1/2)(5)(5)sin60°
    = 25/2 (√3/2) = 25√3/4 cm^2


    height of triangle:
    h^2 + 25/4 = 25
    h^2 = 75/4
    h = √(75/4) = 5√3/2
    area = (1/2)base x height = (1/2)(5)(5√3/2) = 25√3/4

    add up the rectangles and triangles.

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