Question

What is the area of this triangle?

Answer 1

Answer:

A = 18

Step-by-step explanation:

Drop a perpendicular from (x₃, y₃) to point A on the opposite side.

The vertical line containing A is the base of the triangle, and the horizontal line is its height,

The formula for the area of a triangle is  

A = ½bh

b = y₂ - y₁ = 6

h = x₃ - x₁ = 6

A = ½ × 6 × 6 = 18

The area of the triangle is 18.

Answer 2

We use the vertical side as the base: it is a vertical segment, so it's length is the difference of the y coordinates of its endpoints:

$b = y_2-y_1$

The height would be the segment starting from $(x_3,y_3)$, perpendicular to the base. Since this is a horizontal segment, its length is the difference of the x coordinates of its endpoints:

$h = x_3-x_1$

So, the area is given by

$A = \dfrac{bh}{2} = \dfrac{(y_2-y_1)(x_3-x_1)}{2}$