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math

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M and N are the midpoints of the sides of a square. What is the ratio of the area of triangle AMN to the area of the complete square? But the answer has to be in a ratio which is the area of a triangle to the area of the complete square. Also the triangle is in the square at top corner.

  • math -

    Let x = length of side of square
    thus area of square is
    A,square = x^2
    recall that area of triangle is given by
    A,triangle = (1/2)b*h
    where b is the base and h is the height.
    The base and height of the triangle AMN are equal, which is (1/2)x. Thus,
    A,triangle = (1/2)*[(1/2)x]*[(1/2)x]
    A,triangle = (1/8)x^2

    Getting the ratio of areas,
    A,triangle : A,square = (1/8)x^2 : x^2 = 1/8

    hope this helps~ :)

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