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 $x^{2}+$ $x+$ cm²

Explanation:

Step1: Identify base and height

$b = 4x - 2$, $h=2x + 12$

Step2: Substitute into area formula

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

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 the $\frac{1}{2}$

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

Answer:

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