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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