Question

What is the area of triangle LMN

Answer 1

Area of triangle = 1/2 x base x height

Area of the triangle = 1/2 x 4 x 6 = 12 square units

Answer: 12 square units

Answer 2

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.

$\text{Area of triangle}=\frac{1}{2}*\text{Base*Height}$

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.

$\text{Distance}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$\text{Distance between point M and N}=\sqrt{(3--1)^2+(-4--4)^2}$

$\text{Distance between point M and N}=\sqrt{(3+1)^2+(-4+4)^2}$

$\text{Distance between point M and N}=\sqrt{(4)^2+(0)^2}$

$\text{Distance between point M and N}=4$

$\text{Distance between point L and M}=\sqrt{(-1--1)^2+(-4-2)^2}$  

$\text{Distance between point L and M}=\sqrt{(-1+1)^2+(-6)^2}$  

$\text{Distance between point L and M}=\sqrt{0+36}$  

$\text{Distance between point L and M}=6$  

Now let us substitute our side lengths is area formula.

$\text{Area of triangle LMN}=\frac{1}{2}*4*6$

$\text{Area of triangle LMN}=2*6$

$\text{Area of triangle LMN}=12$

Therefore, area of triangle LMN is 12 square units and option A is the correct choice.