Answer:
[tex](4x^2+22x-12)cm^2[/tex]Explanation:
From the given figure:
• The base of the triangle, b = (4x-2) cm
,• The perpendicular height, h = (2x+12) cm
The area of a triangle is calculated using the formula:
[tex]A=\frac{1}{2}bh[/tex]Substitute the given expressions:
[tex]\begin{gathered} A=\frac{1}{2}(4x-2)(2x+12) \\ Factor\text{ }4x-2\implies4x-2=2(2x-1) \\ A=\frac{1}{2}\times2(2x-1)(2x+12) \\ A=(2x-1)(2x+12) \end{gathered}[/tex]Next, open the brackets:
[tex]\begin{gathered} A=2x(2x+12)-1(2x+12) \\ =4x^2+24x-2x-12 \\ =(4x^2+22x-12)cm^2 \end{gathered}[/tex]The area of the triangle is:
[tex](4x^2+22x-12)cm^2[/tex]