Question

an engineer is reviewing the layout of a solar farm. the solar farm shown has 4 small panels, 33 medium panels, and 32 large panels. what is the total area of the farms solar panels? the total area of the small solar panels is represented by 4x² + 24x. the total area of the medium solar panels is represented by 33x² + 272x. the total area of the large solar panels is represented by 32x² + 384x.

Explanation:

Step1: Identify the area - expressions for each type of panel

Small panels area: $4x^{2}+24x$; Medium panels area: $33x^{2}+272x$; Large panels area: $32x^{2}+384x$.

Step2: Calculate the total area

Total area = Area of small panels+Area of medium panels+Area of large panels.
\[

$$\begin{align*} &(4x^{2}+24x)+(33x^{2}+272x)+(32x^{2}+384x)\\ =&(4x^{2}+33x^{2}+32x^{2})+(24x + 272x+384x)\\ =&69x^{2}+680x \end{align*}$$

\]

Answer:

$69x^{2}+680x$