Final answer:
To find the area of a triangle with a given base and height, we can use the formula A = 1/2 * base * height. In this case, the base is 4x+12 and the height is x+6. Simplifying the expression gives us A = 2x^2+18x+36.
Step-by-step explanation:
To find the area of a triangle, we can use the formula A = 1/2 * base * height. In this case, the base is 4x+12 and the height is x+6. So, the area can be expressed as:
A = (1/2)(4x+12)(x+6)
To simplify the expression, we can distribute the 1/2 into the terms:
A = (1/2)(4x)(x+6)+(1/2)(12)(x+6)
Which simplifies to:
A = 2x(x+6)+6(x+6)
Next, we can use the distributive property again to simplify further:
A = 2x^2+12x+6x+36
Combining like terms:
A = 2x^2+18x+36
So, the simplified expression for the area of the triangle is A = 2x^2+18x+36.