The area of a circle of radius r is given by the formula:
![A=\pi\cdot r^2](https://img.qammunity.org/2023/formulas/mathematics/college/c3j55td07q4b6rf8hxaebd9fh4afvxzn0d.png)
On the other hand, the radius r is half the diameter D of the circle:
![r=(D)/(2)](https://img.qammunity.org/2023/formulas/mathematics/college/lhmk5xapcy29peg94dm5wqxlkcly19oyug.png)
Substitute D=10.5 in to find the radius:
![\begin{gathered} r=\frac{10.5\text{ in}}{2} \\ \therefore r=5.25\text{ in} \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/2fg719x6jrgpka25difnzcr3l96viaivxt.png)
Use the value r=5.25 in to find the area of the circle:
![A=\pi\cdot(5.25in)^2](https://img.qammunity.org/2023/formulas/mathematics/college/16qp4cacfber6jfye06tqsj61npsynzccm.png)
Use a calculator to find the numerical value of the expression. We get that:
![A\approx86.59in^2](https://img.qammunity.org/2023/formulas/mathematics/college/kgrt3sx5bjjixrr7me4wd4zwh1gfv31bf3.png)