Question

write an expression to represent the area of the triangle shown below. recall that the area of a triangle is ( a=\frac{1}{2}bh ).

enter your response in the space provided below.

Explanation:

Step1: Identify base and height

Let base $b = 4x + 2$ and height $h=2x - 2$.

Step2: Apply area formula

The area formula of a triangle is $A=\frac{1}{2}bh$. Substitute the values of $b$ and $h$ into the formula: $A=\frac{1}{2}(4x + 2)(2x - 2)$.

Step3: Expand the expression

First, expand $(4x + 2)(2x - 2)$ using FOIL method:
\[

$$\begin{align*} (4x+2)(2x - 2)&=4x\times2x+4x\times(- 2)+2\times2x+2\times(-2)\\ &=8x^{2}-8x + 4x-4\\ &=8x^{2}-4x - 4 \end{align*}$$

\]
Then, multiply by $\frac{1}{2}$: $A=\frac{1}{2}(8x^{2}-4x - 4)=4x^{2}-2x - 2$.

Answer:

$4x^{2}-2x - 2$