Find the area of a triangle whose base is x² + 2x + 4 and whose height is 2x²+2x+6.

A. 3x⁴ + 9x² + 10x + 12

B. x⁴ + 3x³ + 9x² + 10x + 12

C. 3x⁴+3x³ + 9x² + 10x+12

D. x⁴ + 9x² + 10x + 12

Given the following information, the area of the triangle is x⁴+3x³+9x²+10x+12

Step-by-step explanation:

We must know the formula for finding the area of a triangle in order to begin.

Area = 1/2 (b*h)

First we multiply the base and height together.

Base = x² + 2x + 4

Height = 2x² + 2x + 6

(x² + 2x + 4) (2x² + 2x + 6)

Use the foil method to solve this.

2x⁴ + 2x³ + 6x² + 4x³ + 4x² + 12x + 8x² + 8x + 24

Combine like terms.

2x⁴ + 6x³ + 18x² + 20x + 24

Now that we have our product, we have to divide this expression by 2 or 1/2.

(2x⁴ + 6x³ + 18x² + 20x + 24) / 2

So, the area of the triangle is x⁴ + 3x³ + 9x² + 10x + 12