Question

Find the area of the shaded region. Type the coefficients for the quadratic,linear, and constant terms.

Answer 1

`A_(shaded)=2x^2+9x-6`

Explanation:

To find the area of the shaded region, we can calculate the area of the big rectangle and then subtract the little one.

`\begin{gathered} A_{big\text{ rectangle}}=(2x+7)\cdot(x+1) \\ A_{big\text{ rectangle}}=2x^2+2x+7x+7 \\ A_{big\text{ rectangle}}=2x^2+9x+7 \end{gathered}`
`\begin{gathered} A_{little\text{ rectangle}}=4\cdot3 \\ A_{little\text{ rectangle}}=13feet^2 \end{gathered}`

Therefore, the area of the shaded region:

`\begin{gathered} A_(shaded)=2x^2+9x+7-13 \\ A_(shaded)=2x^2+9x-6 \end{gathered}`