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

Base $b = 4x + 2$, height $h=2x - 2$.

Step2: Substitute into area formula

$A=\frac{1}{2}(4x + 2)(2x - 2)$.

Step3: Expand the expression

\[

$$\begin{align*} A&=\frac{1}{2}(4x\times2x-4x\times2 + 2\times2x-2\times2)\\ &=\frac{1}{2}(8x^{2}-8x + 4x-4)\\ &=\frac{1}{2}(8x^{2}-4x - 4)\\ &=4x^{2}-2x - 2 \end{align*}$$

\]

Answer:

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