Exercise:
Berechne den Flächeninhalt des Dreiecks ABC mit den Punkten Apgfmathprnumberax pgfmathprnumberay pgfmathprnumberaz Bpgfmathprnumberbx pgfmathprnumberby pgfmathprnumberbz und Cpgfmathprnumbercx pgfmathprnumbercy pgfmathprnumbercz.

Solution:
center tikzpicturescale. drawthick-stealth --nodeanchornorth eastz; drawthick-stealth --nodeanchorsouthy; drawthick -stealth --nodeanchorwestx; coordinate A at axayaz; coordinate B at bxbybz; coordinate C at cxcycz; fill A circle .pt nodeanchornorth westApgfmathprnumberaxpgfmathprnumberay pgfmathprnumberaz; fill B circle .pt nodeanchornorth westBpgfmathprnumberbxpgfmathprnumberby pgfmathprnumberbz; fill C circle .pt nodeanchornorth westCpgfmathprnumbercxpgfmathprnumbercy pgfmathprnumbercz; draw - thickA--B; draw - thickA--C; draw B--C; drawfillblueopacity. A--B--C; tikzpicture center Der erste Schritt ist es die Vektoren zu berechnen. Man rechnet den Endpunkt minus den Anfangspunkt. vecAB B - A pmatrixpgfmathprnumberbx pgfmathprnumberby pgfmathprnumberbzpmatrix - pmatrixpgfmathprnumberax pgfmathprnumberay pgfmathprnumberazpmatrix pmatrixpgfmathprnumberabx pgfmathprnumberaby pgfmathprnumberabzpmatrix vecAC C - Apmatrixpgfmathprnumbercx pgfmathprnumbercy pgfmathprnumberczpmatrix - pmatrixpgfmathprnumberax pgfmathprnumberay pgfmathprnumberazpmatrix pmatrixpgfmathprnumberacx pgfmathprnumberacy pgfmathprnumberaczpmatrix Die Fläche des Parallelogramm ist die länge des Kreuzproduntks dieser zwei Vektoren. A_p |vecAB times vecAC| Biggl|pmatrixpgfmathprnumbersolx pgfmathprnumbersoly pgfmathprnumbersolzpmatrixBiggl| sqrtpgfmathprnumbersolx^ + pgfmathprnumbersoly^ + pgfmathprnumbersolz^ sqrtpgfmathprnumberl pgfmathprnumbersl Die Fläche des Dreieck das wir suchen ist die halbe Fläche des Parallelogramms. A_Delta fracpgfmathprnumbersl pgfmathprnumbersol