Use calculus to find the area A of the triangle with the given vertices.
(0, 0), (6, 5), (4, 8)
This is a two-part question. The first part involves finding the equations of the lines connecting the three points. The second part involves calculating the areas. Two of the lines pass through the origin (0,0), and hence have equations y
= mx. Let’s call A(0,0), B(4,8) and C(6,5). Line AB is y = 2x (8-0 / 4-0) and Line AC is y= Line BC has an equation of y = mx+b. m = (5-8 / 6-4) = -3/2. b = 5− = 14.
The second part involves two regions: the area between AB and AC from 0 to 4, and the area between BC and AC from 4 to 6. We can set up the integral statement as follows, using the formula for the area between two functions