Find the area of triangle MAN, in square units, given that M(5,2014), A(11,23), N(11,32). Show your work. Thanks!?

3 Answers

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  • MA =

    sqrt((2014 - 23)^2 + (5 - 11)^2) =

    sqrt(1991^2 + (-6)^2) =

    sqrt((2000 - 9)^2 + 36) =>

    sqrt(4000000 - 36000 + 81 + 36) =>

    sqrt(4000000 - 36000 + 117) =>

    sqrt(1000 * (4000 - 36) + 117) =>

    sqrt(1000 * 3964 + 117) =>

    sqrt(3964117)

    MN =>

    sqrt((2014 - 32)^2 + (5 - 11)^2) =>

    sqrt(1982^2 + (-6)^2) =>

    sqrt((2000 - 18)^2 + 36) =>

    sqrt(4000000 - 72000 + 324 + 36) =>

    sqrt(4000000 - 72000 + 360) =>

    sqrt(1000 * (4000 - 72) + 360) =>

    sqrt(1000 * 3928 + 360) =>

    sqrt(3928360) =>

    2 * sqrt(982090)

    AN =>

    sqrt((32 - 23)^2 + (11 - 11)^2) =>

    sqrt(9^2 + 0^2) =>

    9

    s = (9 + 2 * sqrt(982090) + sqrt(3964117)) / 2

    sqrt(s * (s - a) * (s - b) * (s - c)) =>

    sqrt((1/2)^4 * (9 + 2 * sqrt(982090) + sqrt(3964117)) * (9 + 2 * sqrt(982090) + sqrt(3964117) - 18) * (9 + 2 * sqrt(982090) + sqrt(3964117) - 4 * sqrt(982090)) * (9 + 2 * sqrt(982090) - sqrt(3964117)) =>

    (1/2)^2 * sqrt((9 + 2 * sqrt(982090) + sqrt(3964117)) * (-9 + 2 * sqrt(982090) + sqrt(3964117)) * (9 - 2 * sqrt(982090) + sqrt(3964117)) * (9 + 2 * sqrt(982090) - sqrt(3964117))

    (9 + 2 * sqrt(982090) + sqrt(3964117)) * (9 + 2 * sqrt(982090) - sqrt(3964117)) * (sqrt(3964117) - (9 - 2 * sqrt(982090))) * (sqrt(3964117) + (9 - 2 * sqrt(982090))) =>

    ((9 + 2 * sqrt(982090))^2 - 3964117) * (3964117 - (9 - 2 * sqrt(982090))^2) =>

    -(3964117 - (81 + 36 * sqrt(982090) + 4 * 982090)) * (3964117 - (81 - 36 * sqrt(982090) + 4 * 982090)) =>

    -(3964117 - 81 - 4 * 982090 - 36 * sqrt(982090)) * (3964117 - 81 - 4 * 982090 + 36 * sqrt(982090)) =>

    -(35676 - 36 * sqrt(982090)) * (35676 + 36 * sqrt(982090)) =>

    -(35676^2 - 36^2 * 982090) =>

    (982090 * 36^2 - 35676^2) =>

    11664

    (1/2)^2 * sqrt(11664) =>

    (1/4) * sqrt(4 * 4 * 729) =>

    (1/4) * 4 * sqrt(729) =>

    sqrt(729) =>

    27

  • alex
    Lv 7
    6 months ago

    AN = 9

    The altitude MH = 6

    Area = (1/2)(6)(9)=27

  • 6 months ago

    distance between two points

    d = √(Δx² + Δy²)

    use this to get the length of each side.

    MA = √(6² + (2014-23)²)

    MN = √(6² + (2014-32)²)

    AN = √(0 + 9²) = 9

    then use this to get the area.

    A = √[s(s–a)(s–b)(s–c)]

    where s = (a+b+c)/2

    a,b,c are the sides of the triangle

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