Question

Calcule a área do triângulo a seguir:

4
6
7
8 ​

Answer 1

Resposta:

D)8

Explicação passo a passo:

A(1,3)    B(7,1)       C(3,5)

║1      3      1║ 1      3      multiplicando as diagonais principais;

 7      1       1    7     1        1*1*1+3*1*3+1*7*5=1+9+35=45

 3      5      1    3     5       multiplicando as diagonais secundárias;

                                        1*1*3+1*1*5+3*7*1=3+5+21=29

subtraíndo as diagonais;

45-29=16

área =1/2*║16║

A=1/2*16

A=8

Answer 2

$\Large\boxed{\begin{array}{l}\sf Sejam~A(x_A,y_A)~B(x_B,y_B)~e~C(x_C,y_C)\\\sf os~v\acute ertices~de~um~tri\hat angulo.A~\acute area\\\sf deste~tri\hat angulo~\acute e~dada~por\\\sf A=\dfrac{|det~M|}{2}~onde\\\\\sf M=\begin{vmatrix}\sf x_A&\sf y_A&\sf 1\\\sf x_B&\sf y_B&\sf1\\\sf x_C&\sf y_C&\sf1\end{vmatrix} \end{array}}$$\Large\boxed{\begin{array}{l}\sf A(1,3)~B(7,1)~C(3,5)\\\sf M=\begin{vmatrix}\sf 1&\sf3&\sf1\\\sf7&\sf1&\sf1\\\sf3&\sf5&\sf1\end{vmatrix}\\\\\sf det~M= 1\cdot(1-5)-3\cdot(7-3)+1\cdot(35-3)\\\sf det~M=-4-12+32\\\sf det~M=16\\\sf A=\dfrac{|det~M|}{2}\\\\\sf A=\dfrac{16}{2}\\\\\sf A=8~u\cdot a\end{array}}$