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Find the area of the triangle with vertices at the points given \((1, 0), (6, 0), (4, 3).\)
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MathsClass 12

Find the area of the triangle with vertices at the points given \((1, 0), (6, 0), (4, 3).\)

Answer

\(7.5\ unit^2\)
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Solution

Given, the points \((1, 0), (6, 0), (4, 3).\)
To find: The area of the triangle
Solution:
We have, the points \((1, 0), (6, 0), (4, 3).\)
We know that, area of triangle \(=\dfrac{1}{2}\left| {\begin{array}{*{20}{c}} {{x_1}}&{{y_1}}&1 \\ {{x_2}}&{{y_2}}&1 \\ {{x_3}}&{{y_3}}&1 \end{array}} \right|\)
Here, \(x_1=1,x_2=6,x_3=4\) and \(y_1=0,y_2=0,y_3=3\)
\(\therefore\) Area of triangle \(=\dfrac{1}{2} \left| {\begin{array}{*{20}{c}} 1&0&1 \\ 6&0&1 \\ 4&3&1 \end{array}} \right|\)
\(= \dfrac{1}{2}[1(0-3)-0(6-4)+1(18-0)]\)
\(= \dfrac{1}{2}[-3-0+18]\)
\(=\dfrac{15}{2}\)
\(=7.5\ unit^2\)
Hence, the area of the triangle is \(7.5\ unit^2.\)
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