Alg6.10

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Find the area of the triangle formed by (2,4),(2,6),(2+{\sqrt  {3}},5)\,

The formula for finding the area of the traingle formed by (x_{1},y_{1}),(x_{2},y_{2}),(x_{3},y_{3})\, is {\frac  {1}{2}}|[x_{1}(y_{2}-y_{3})+x_{2}(y_{3}-y_{1})+x_{3}(y_{1}-y_{2})]|\,

Aplying the formula,we get

{\frac  {1}{2}}|[2(6-5)+2(5-4)+(2+{\sqrt  {3}})(4-6)]|\,

{\frac  {1}{2}}|2+2-4-2{\sqrt  {3}}|\,

{\frac  {1}{2}}|-2{\sqrt  {3}}|\,

Hence the area of the triangle is {\sqrt  {3}}\,.


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