Chapter 10 - Parametric Equations and Polar Coordinates - 10.4 Exercises - Page 692: 5

$\pi ^{2}\approx 9.87$

$A=\int ^{2\pi }_{0}\dfrac {1}{2}\left[ r^2\right] d\theta =\int ^{2\pi }_{0}\dfrac {1}{2}\theta d\theta =\left[ \dfrac {1}{4}\theta ^{2}\right] ^{2\pi }_{0}=\dfrac {4\pi ^{2}}{4}-0=\pi ^{2}\approx 9.87$