Use the formula for the area of a circle:
![A=\pi\cdot r^2](https://img.qammunity.org/2023/formulas/mathematics/college/c3j55td07q4b6rf8hxaebd9fh4afvxzn0d.png)
First, we need to find the radius r. Since the radius is half the diameter, then:
![\begin{gathered} r=\frac{10.5\text{ in}}{2} \\ \therefore r=5.25in \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/r597ly6flxd1vmou7plor8zb4j2bt55m6r.png)
Substitute the value for r in the formula for the area of the circle:
![\begin{gathered} A=\pi\cdot(5.25in)^2 \\ \approx86.6in^2 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/g29255y18ysgwzmcbvo5jygyqwi0cbs1ix.png)
Therefore, the area of a circle of diameter 10.5 in is approximately 86.6 squared inches.