Middle School

Find the area of a triangle whose base is [tex]x^2 + 2x + 4[/tex] and whose height is [tex]2x^2 + 2x + 6[/tex].

A. [tex]3x^4 + 9x^2 + 10x + 12[/tex]
B. [tex]x^4 + 3x^3 + 9x^2 + 10x + 12[/tex]
C. [tex]3x^4 + 3x^3 + 9x^2 + 10x + 12[/tex]
D. [tex]x^4 + 9x^2 + 10x + 12[/tex]

Answer :

Answer:

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

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