Question

What is the expression for the area of a triangle with a height of 3x² units and a base of 6x² + 5x? The formula for area of the triangle is A = 1/2 b h

Answer 1

We have the formula for the area of the triangle as:

`A=(1)/(2)\cdot b\cdot h`

If h and b are functions of x, we can replace them in the area function and have the area in function of x:

`\begin{gathered} h=3x^2 \\ b=6x^2+5x \end{gathered}`
`\begin{gathered} A=(1)/(2)\cdot b\cdot h \\ A=(1)/(2)(6x^2+5x)(3x^2) \\ A=(1)/(2)(18x^4+15x^3) \\ A=9x^4+(15)/(2)x^3 \end{gathered}`

Answer: A = 9*x^4 + (15/2)*x^3