Como son tres puntos A ( - 2, 5), B ( - 7, - 5) y C (6, 0) debe ser un triangulo, para hallar su area y perimetro hallemos sus lados(que son distancias)
<img src="https://tex.z-dn.net/?f=%20d%28AB%29%3D%5Csqrt%7B%20%28-5-5%29%5E%7B2%7D%20%2B%20%28-7-%28-2%29%29%5E%7B2%7D%20%7D%20" />
<img src="https://tex.z-dn.net/?f=%20d%28AB%29%3D%5Csqrt%7B%20%28-10%29%5E%7B2%7D%20%2B%20%28-5%29%5E%7B2%7D%20%7D%20" />
<img src="https://tex.z-dn.net/?f=%20d%28AB%29%3D%5Csqrt%7B%20100%20%2B%2025%20%7D%20" />
<img src="https://tex.z-dn.net/?f=%20d%28AB%29%3D%5Csqrt%7B%20125%20%7D%20" />
<img src="https://tex.z-dn.net/?f=%20d%28AB%29%3D11.1803%20" />
<img src="https://tex.z-dn.net/?f=%20d%28BC%29%3D%5Csqrt%7B%20%280-%28-5%29%29%5E%7B2%7D%20%2B%20%286-%28-7%29%29%5E%7B2%7D%20%7D%20" />
<img src="https://tex.z-dn.net/?f=%20d%28BC%29%3D%5Csqrt%7B%20%285%29%5E%7B2%7D%20%2B%20%2813%29%5E%7B2%7D%20%7D%20" />
<img src="https://tex.z-dn.net/?f=%20d%28BC%29%3D%5Csqrt%7B%2025%2B%20169%20%7D%20" />
<img src="https://tex.z-dn.net/?f=%20d%28BC%29%3D%5Csqrt%7B%20194%20%7D%20" />
<img src="https://tex.z-dn.net/?f=%20d%28BC%29%3D13.9283%20" />
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Usaremos la formula de heron , con los lados del triangulo
AB = 11.
1803, BC = 13.
9283 , CA) = 9.
4339 , y p el semiperimetro
perimetro = AB + BC + CA = 34.
5425
semiperimetro = (AB + BC + CA) / 2
semiperimetro = 34.
5425 / 2
semiperimetro = 17.
27125
la formula de heron
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52.
49935.
←esta es el area.