Answer
$\mathrm{a}$.
$A(\displaystyle \frac{1}{3})\approx 1.26\ \mathrm{f}\mathrm{t}^{2}$
$\mathrm{b}$.
$A(\displaystyle \frac{1}{2})\approx 1.73\ \mathrm{f}\mathrm{t}^{2}$
$\mathrm{c}$.
$A(\displaystyle \frac{2}{3})\approx 1.99\ \mathrm{f}\mathrm{t}^{2}$
Work Step by Step
Substitute x=(given value) into the expression for A.
$\mathrm{a}$.
$A(\displaystyle \frac{1}{3})=4\cdot\frac{1}{3}\sqrt{1-(\frac{1}{3})^{2}}$
$=\displaystyle \frac{4}{3}\sqrt{\frac{8}{9}}$
$=\displaystyle \frac{4}{3}\cdot\frac{2\sqrt{2}}{3}$
$=\displaystyle \frac{8\sqrt{2}}{9}\approx 1.26\ \mathrm{f}\mathrm{t}^{2}$
$\mathrm{b}$.
$A(\displaystyle \frac{1}{2})=4\cdot\frac{1}{2}\sqrt{1-(\frac{1}{2})^{2}}$
$=2\sqrt{\dfrac{3}{4}}$
$=2\displaystyle \cdot\frac{\sqrt{3}}{2}$
$=\sqrt{3}\approx 1.73\ \mathrm{f}\mathrm{t}^{2}$
$\mathrm{c}$.
$A(\displaystyle \frac{2}{3})=4\cdot\frac{2}{3}\sqrt{1-(\frac{2}{3})^{2}}$
$=\displaystyle \frac{8}{3}\sqrt{\frac{5}{9}}$
$=\displaystyle \frac{8}{3}\cdot\frac{\sqrt{5}}{3}$
$=\displaystyle \frac{8\sqrt{5}}{9}\approx 1.99\ \mathrm{f}\mathrm{t}^{2}$