Question

dacă A(1,0),B(-1,0)și C(0,1),atunci aria triunghiului ABC este...?

Answer 1

Răspuns:

Explicație pas cu pas:

AB = √[(-1 -1)^2 + (0 - 0)^2] = √4 = 2

AC = √[(0 - 1)^2 + (1 - 0)^2] = √2

BC = √[(0 + 1)^2 + (1 - 0)^2] = √2

P = AB + AC + BC = 2 + √2 + √2 = 2 + 2√2

p = P : 2 = (2 + 2√2) : 2 = 1 + √2

A = √p(p-a)(p-b)(p-c)

p(p-a)(p-b)(p-c) = (1 + √2)(1 + √2 - 2)(1 + √2 - √2)(1 + √2 - √2)

= (1 + √2)(√2 - 1)*1*1 = (√2 + 1)(√2 - 1) = 2 - 1 = 1

A = √1 = 1

Answer 2

A(1,0) B(-1,0) C(0,1)

Aria=1/2×|delta|

delta=|1 0 1|

|-1 0 1|

|0 1 1|

1 0 1

-1 0 1

=0-1+0-0-1-0

= -2

Aria= 1/2×|-2|

A=1/2×2

A=2/2

A=1