Find the area of tangle
$A (a t_{1}^{2}, {2 a t}_{2}), B ({a t}_{2}^{2}, {2 a t}_{2}), C ({a t}_{3}^{2}, {2 a t}_{3})$

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Solution

$A (a t_{1}^{2}, 2 a t_{2}), B (a t_{2}^{2}, 2 a t_{2}), C (a t_{3}^{2}, 2 a t_{3})$

Area $= \frac{1}{2} ∣ ∣ ∣ ∣ ∣ \begin{matrix} a t_{1}^{2} & 2 a t_{1} & 1 a t_{2}^{2} & 2 a t_{2} & 1 a t_{3}^{2} & 2 a t_{3} & 1 \end{matrix} ∣ ∣ ∣ ∣ ∣$

$⟹$ Area $= a^{2} ∣ ∣ ∣ ∣ ∣ \begin{matrix} t_{1}^{2} & t_{1} & 1 t_{2}^{2} & t_{2} & 1 t_{3}^{2} & t_{3} & 1 \end{matrix} ∣ ∣ ∣ ∣ ∣$

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