Chapter 8.2, Problem 28PPE

To determine

To find: The area of the yellow part of the tabletop in factored form.

Answer to Problem 28PPE

  $9x^2(4\pi -1)$

Explanation of Solution

Given information: A circular table is painted yellow with a red square in the middle. The radius of the tabletop is 6x. The side length of the red square is 3x.

  

Calculation:

The area of the red square is,

  $\begin{array}{l}{\text{(side)}}^2\\ $ ={(3x)}^2$=9x^2\end{array}$

The total area of the circular table including the red square is,

  $\begin{array}{l}$ \pi {(\text{radius)}}^2$$ =\pi {(6x)}^2$=36\pi x^2\end{array}$

Then, area of the yellow part of the tabletop is,

  $\begin{array}{l}36\pi x^2-9x^2\\ =9x^2(4\pi -1)[\text{factoring out the GCF]}\end{array}$

Thus, the area of the yellow part of the tabletop is $9x^2(4\pi -1)$ .