Question

find a simplified expression to represent the area of the triangle. the area formula for a triangle is $\frac{1}{2}bh$, where $b$ is the base and $h$ is the height.
(2x + 12) cm
(4x - 2) cm
the expression that represents the area of this triangle is $square x^{2}+square x+square$ $cm^{2}$.

Explanation:

Step1: Identify base and height

Base $b=(4x - 2)$ cm, height $h=(2x + 12)$ cm.

Step2: Apply area formula

$A=\frac{1}{2}bh=\frac{1}{2}(4x - 2)(2x + 12)$.

Step3: Expand the product

First, expand $(4x - 2)(2x + 12)$ using FOIL method:
$(4x - 2)(2x + 12)=4x\times2x+4x\times12-2\times2x - 2\times12=8x^{2}+48x-4x - 24=8x^{2}+44x - 24$.
Then, $A=\frac{1}{2}(8x^{2}+44x - 24)$.

Step4: Distribute $\frac{1}{2}$

$A=\frac{1}{2}\times8x^{2}+\frac{1}{2}\times44x-\frac{1}{2}\times24 = 4x^{2}+22x - 12$ cm².

Answer:

$4x^{2}+22x - 12$