Take into account that the area of the triangle is given by:
[tex]A=\frac{1}{2}bh[/tex]where,
b: base length of the triangle = 2ac^2
h: height of the triangle = 6 + 2ac^2
in this case, a = 4 and c = 2.
Replace the given expressions for b and h and then replace the values of a and b:
[tex]\begin{gathered} A=\frac{1}{2}(2ac^2)(6+2ac^2) \\ A=\frac{1}{2}(2\cdot4\cdot2^2)(6+2\cdot4\cdot2^2) \\ A=\frac{1}{2}(32)(6+32) \\ A=\frac{1}{2}(32)(38) \\ A=608 \end{gathered}[/tex]Hence, the area of the given triangle is 608 cm^2