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Answer 1 · 2018-01-22T13:30:55

Area of triangle #color(brown)(A_t = 316.4992)#

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Given #A (-13, 2), B (5,17), C(22, -4)#

#a = sqrt((22-5)^2 + (-4-17)^2) = 27.0185#

#b = sqrt((22+13)^2 + (-4-2)^2) = 35.5106#

#c = sqrt((5+13)^2 + (17-2)^2) = 23.4307#

Semiperimeter #s = (a + b + c) / 2 = (27.0185 + 35.5106 + 23.4307 ) / 2#

#color(blue)(42.9799)#

Area of triangle

#A_t = sqrt ( s ( s-a) ( s-b) (s-c))#

#A_t = sqrt(42.9799 * (42.9799-27.0185) * (42.9799 - 35.5106) * (42.9799-23.4377))#

#A_t = sqrt(42.9799 * 15.9614 * 7.4693 * 19.5492)#

#color(brown)(A_t = 316.4992)#