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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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QuestionMathsClass 12

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

$$7.5\ unit^2$$
4.6
4.6

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 $$7.5\ unit^2.$$