To find the area of a triangle, we use the formula:
[tex]\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \][/tex]
Given that the base of the triangle is [tex]\( 3x^2y^2 \)[/tex] and the height is [tex]\( 4x^4y^3 \)[/tex], we can substitute these values into the formula.
First, let's plug in the values for the base and height:
[tex]\[ \text{Area} = \frac{1}{2} \times (3x^2y^2) \times (4x^4y^3) \][/tex]
Next, we perform the multiplication inside the parentheses. When multiplying these terms, we multiply the coefficients (numerical parts) and add the exponents of like variables:
[tex]\[ (3x^2y^2)(4x^4y^3) = 3 \times 4 \times x^{2+4} \times y^{2+3} \][/tex]
[tex]\[ = 12x^6y^5 \][/tex]
So, our expression now looks like this:
[tex]\[ \text{Area} = \frac{1}{2} \times 12x^6y^5 \][/tex]
Finally, we multiply by [tex]\(\frac{1}{2}\)[/tex]:
[tex]\[ \frac{1}{2} \times 12x^6y^5 = 6x^6y^5 \][/tex]
Therefore, the area of the triangle is:
[tex]\[ \boxed{6x^6y^5} \][/tex]
