Answer:
A. 12 square units.
Step-by-step explanation:
We have been given graph of a triangle and we are asked to find the area of our given triangle.
Since we know that area of a triangle is half the product of height of triangle and base of the triangle.
[tex]\text{Area of triangle}=\frac{1}{2}*\text{Base*Height}[/tex]
We can see that MN is base of our triangle and LM is height of triangle, so let us find lengths of MN and LM using distance formula.
[tex]\text{Distance}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]\text{Distance between point M and N}=\sqrt{(3--1)^2+(-4--4)^2}[/tex]
[tex]\text{Distance between point M and N}=\sqrt{(3+1)^2+(-4+4)^2}[/tex]
[tex]\text{Distance between point M and N}=\sqrt{(4)^2+(0)^2}[/tex]
[tex]\text{Distance between point M and N}=4[/tex]
[tex]\text{Distance between point L and M}=\sqrt{(-1--1)^2+(-4-2)^2}[/tex]
[tex]\text{Distance between point L and M}=\sqrt{(-1+1)^2+(-6)^2}[/tex]
[tex]\text{Distance between point L and M}=\sqrt{0+36}[/tex]
[tex]\text{Distance between point L and M}=6[/tex]
Now let us substitute our side lengths is area formula.
[tex]\text{Area of triangle LMN}=\frac{1}{2}*4*6[/tex]
[tex]\text{Area of triangle LMN}=2*6[/tex]
[tex]\text{Area of triangle LMN}=12[/tex]
Therefore, area of triangle LMN is 12 square units and option A is the correct choice.
