To determine how many pavers Parker needs to build the patio, we can follow these steps:
1. Calculate the Area of the Patio:
The patio is a rectangle with a length of 16 feet and a width of 8 feet. Using the area formula for a rectangle [tex]\(A = l \times w\)[/tex]:
[tex]\[
A_{\text{patio}} = 16 \, \text{feet} \times 8 \, \text{feet} = 128 \, \text{square feet}
\][/tex]
So, the area of the patio is 128 square feet.
2. Calculate the Area of One Paver:
Each paver is a square with a side length of 2 feet. Using the area formula for a square [tex]\(A = s^2\)[/tex]:
[tex]\[
A_{\text{paver}} = (2 \, \text{feet})^2 = 4 \, \text{square feet}
\][/tex]
So, the area of one paver is 4 square feet.
3. Determine the Number of Pavers Needed:
To find out how many pavers are needed to cover the entire patio, we divide the total area of the patio by the area of one paver:
[tex]\[
\text{Number of Pavers} = \frac{A_{\text{patio}}}{A_{\text{paver}}} = \frac{128 \, \text{square feet}}{4 \, \text{square feet}} = 32
\][/tex]
So, Parker needs 32 pavers to build the patio.
Therefore, the answer is:
[tex]\[
\boxed{32}
\][/tex]
