Question

area of the triangle whose vertices are (1,1)(2,2)(5,4)

Answer 1

Answer:

1/2(1(2-4)+2(4-1)+5(1-2))

1/2(-2+6-5)

1/2(-1)

1/2(1) as it lie between bar and there can no negative value of area

1/2 is answer

Answer 2

Hello !!

The area of a triangle can be give with the half of the module of your vertices.

$\left(\begin{array}{ccc}1&1&1\\2&2&1\\5&4&1\end{array}\right)\begin{array}{cc}1&1\\2&2\\5&4\end{array}$

Now, you calculate the determinant.

$\mathsf{Det=2+5+8-10-4-2} \\\\\\ \mathsf{Det=2+5+8-10-6} \\\\\\ \mathsf{Det=2+5+8-16} \\\\\\ \mathsf{Det=2+5-8} \\\\\\ \mathsf{Det=2-3} \\\\\\ \mathsf{Det=-1}$

In last step, you find the area.

$\mathsf{A=\dfrac{|Det|}{2}} \\\\\\ \mathsf{A=\dfrac{|-1|}{2}} \\\\\\ \mathsf{A=\dfrac{1}{2}} \\\\\\ \boxed{\bf\blue{\mathsf{A=0.5 \:ua}}}$

Final result: 0.5 ua

I hope I have collaborated !