Question

find the area. simplify your answer. 2x - 4

Explanation:

Step1: Recall the formula for the area of a triangle

The formula for the area of a triangle is \(A=\frac{1}{2}\times base\times height\).

Step2: Identify the base and height

Here, the base \(b = 4\) and the height \(h=2x - 4\).

Step3: Substitute into the formula

Substitute \(b = 4\) and \(h = 2x-4\) into \(A=\frac{1}{2}\times b\times h\), we get \(A=\frac{1}{2}\times4\times(2x - 4)\).
First, simplify \(\frac{1}{2}\times4 = 2\). Then, use the distributive property \(a(b + c)=ab+ac\) (here \(a = 2\), \(b=2x\), \(c=- 4\)), so \(A=2\times2x-2\times4\).

Step4: Calculate the result

\(2\times2x=4x\) and \(2\times4 = 8\), so \(A = 4x-8\).

Answer:

\(4x - 8\)