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If the area of a square is 100 cm. What is the area of each triangle produced if you draw two diagonals in the square?

  • geometry -

    Area of square = side s^2
    100 = s^2
    s = 10

    The diagonals of a square bisect each other and meet at 90 degrees.

    The diagonals of a square bisect its angles.

    The diagonals of a square are perpendicular.

    The diagonals of a square are equal.

    This means that the two diagonals create 4 triangles of equal area.

    To find the length of the equal diagonals d,

    d = s * (sqrt(2))
    s = 10
    d = 10(sqrt(2))
    d/2 = 10(sqrt(2))/2 = 5(sqrt(2))

    Since, the diagonals of a square bisect each other and meet at 90 degrees, the four triangles are each 45-45-90 degrees.

    side = hypotenuse = 10
    leg = 1/2 d = 5(sqrt(2))
    leg = 1/2 d = 5(sqrt(2))

    One leg = height
    One leg = base
    Area = 1/2 bh
    A = 1/2 5(sqrt(2)) * 5(sqrt(2))
    A = 1/2 * 50
    A = 25 cm^2

    Each triangle's area is,
    25 cm^2

    Draw a picture so you can follow the above.

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