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

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• 6 months ago

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