Question

Determine a área do quadrilátero que possui os vértices A (6,3) , B (11,4) , C (9,6) e D (3,4)

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo-a-passo:

$\mathsf{A_{ABCD} = \dfrac{|\:D_1\:| + |\:D_2\:|}{2}}$

$\mathsf{D_1 = }\begin{bmatrix}\cancel3&\cancel4&\cancel1\\\cancel6&\cancel3&\cancel1\\\cancel9&\cancel6&\cancel1\end{bmatrix}$

$\mathsf{D_1 = (9 + 36 + 36) - (27 + 18 + 24)}$

$\mathsf{D_1 = 81 - 69}$

$\mathsf{D_1 = 12}$

$\mathsf{D_2 = }\begin{bmatrix}\cancel11&\cancel4&\cancel1\\\cancel6&\cancel3&\cancel1\\\cancel9&\cancel6&\cancel1\end{bmatrix}$

$\mathsf{D_2 = (33 + 36 + 36) - (27 + 66 + 24)}$

$\mathsf{D_2 = 105 - 117}$

$\mathsf{D_2 = -12}$

$\mathsf{A_{ABCD} = \dfrac{|\:12\:| + |\:-12\:|}{2}}$

$\mathsf{A_{ABCD} = \dfrac{12 + 12}{2}}$

$\mathsf{A_{ABCD} = \dfrac{24}{2}}$

$\boxed{\boxed{\mathsf{A_{ABCD} = 12}}}$