Math

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A children's play area is triangular. The sides of the play area measure 90m, 225m and 255m respectively. Calculate the area of the play area.

  • Math -

    The semiperimeter of a triangle is half its perimeter.

    The formula for the semiperimeter of a triangle with side lengths a, b, and c is:

    s = ( a + b + c ) / 2


    The area of a triangle can also be calculated from its semiperimeter using Heron's formula:

    A = [ sqrt s * ( s - a ) * ( s - b ) * ( s - c ) ]


    In this case:

    a = 90

    b = 225

    c = 255


    s = ( 90 + 225 + 255 ) / 2 = 570 / 2 = 285


    A = sqrt [ s * ( s - a ) * ( s - b ) * ( s - c ) ]

    A = sqrt [ 285 * ( 285 - 90 ) * ( 285 - 225 ) * ( 285 - 255 ) ]

    A = sqrt ( 285 * 195 * 60 * 30)

    A = sqrt ( 10003500 )

    A = 10001.7498469 m ^ 2


    approx. A = 10001.75 m ^ 2

  • Math -

    A = sqrt [ s * ( s - a ) * ( s - b ) * ( s - c ) ]

  • Math -

    Thanks so much

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