Question

What is the area of this triangle?

Answer 1

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 = (bh)/(2) = ((y_2-y_1)(x_3-x_1))/(2)`

Answer 2

A = 18

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.