Question

São dados os pontos A (1,5) B(1,1) e C (5,5)
a) calcule o perímetro do triângulo ABC ?
b) Determine a área do triângulo?

Answer 1

a)
$1 .5 + 1.1 + 5.5 = 81$
b)
$(1.5 + 1.1) \times 5.5 \\ 2.6 \times 5.5 = 11.30$

Answer 2

a)

$\mathsf{d_{A, B}=\sqrt{{(1-1)}^{2}+{(1-5)}^{2}}=\sqrt{16}=4}$

$\mathsf{d_{A, C}=\sqrt{{(5-1)}^{2}+{(5-5)}^{2}}=\sqrt{16}=4}$

$\mathsf{d_{B,C}=\sqrt{{(5-1)}^{2}+{(5-1)}^{2}}=\sqrt{2.16}=4\sqrt{2}}$

$\mathsf{2p=\overline{AB}+\overline{AC}+\overline{BC}}\\\mathsf{2p=4+4+4\sqrt{2}=8+4\sqrt{2}}$

b)

$\mathsf{T=\begin{vmatrix}1&5&1\\1&1&1\\5&5&1\end{vmatrix}}$

$\mathsf{det\,T=1(1-5)-5(1-5)+1(5-5)}$

$\mathsf{det\,T=-4+20=16}$

$\mathsf{A_{triângulo} =\dfrac{1}{2}.|det\,T|}$

$\mathsf{A_{triângulo}=\dfrac{1}{2}.|16|}$

$\mathsf{A_{triângulo}=\dfrac{1}{2}.16=8}$