Final answer:
The height of the triangle is nine more than four times its base. The area of the triangle can be calculated using the expression 2b^2 + 9b.
Step-by-step explanation:
The height of a triangle is nine more than four times its base. Let's use the variable 'b' to represent the base and 'h' to represent the height.
Based on the given information, we can write the equation: h = 4b + 9
To find the area of a triangle, we use the formula A = 1/2 * base * height. Substituting the values, we have A = 1/2 * b * (4b + 9)
Simplifying the equation, we have A = 2b^2 + 9b
Therefore, the area of the triangle is given by the expression 2b^2 + 9b.