The base of a triangle in terms of x is: 2^2+4x+2 and the height is x^2+3x-4

Area=1/2(2x^2+4x+2) (x^2+3x-4)= 6x^2+2 (x^2+3x-4)

Trying to find the area and not sure which direction to go

If you're trying to find the expression for the area, you have for some reason combined the x^2 and x terms (a no-no). The area is

1/2(2x^2+4x+2)(x^2+3x-4)
(x+1)^2 (x+4)(x-1)

As you say, not sure which way to go. You have an expression for the area. Was there some other objective?

re-evaluate your terms. I got x^4 +5x^3 -x^2 -5x-4.

my work:
.5(2x^2 +4x +2)(x^2 +3x -4)=.5(2x^4+6x^3-8x^2+4x^3+4x^2 -16x+2x^2 +6x-8)

To find the area of the triangle, we can use the formula:

Area = (1/2) * base * height

In this case, we are given that the base of the triangle is 2^2 + 4x + 2, and the height is x^2 + 3x - 4.

Let's substitute these values into the formula:

Area = (1/2) * (2^2 + 4x + 2) * (x^2 + 3x - 4)

We can simplify this expression:

Area = (1/2) * (4 + 4x + 2) * (x^2 + 3x - 4)

Area = (1/2) * (6 + 4x) * (x^2 + 3x - 4)

Now, let's distribute the (1/2) across the terms inside the parentheses:

Area = (1/2) * 6 * (x^2 + 3x - 4) + (1/2) * 4x * (x^2 + 3x - 4)

Area = 3 * (x^2 + 3x - 4) + 2x * (x^2 + 3x - 4)

Area = 3x^2 + 9x - 12 + 2x^3 + 6x^2 - 8x + 2x^2 + 6x - 8

Finally, let's combine like terms:

Area = 2x^3 + 9x^2 + 23x - 20

So, the area of the triangle is given by the expression: 2x^3 + 9x^2 + 23x - 20.