Solution
= Solution
Each radial segment from $0$ to $1+\cos\theta$ lies inside the <cardioid>. Integrating the <polar area element> gives
$$
\mathcal A=\int_0^{2\pi}\int_0^{1+\cos\theta}r\,dr\,d\theta
=\frac12\int_0^{2\pi}(1+2\cos\theta+\cos^2\theta)\,d\theta.
$$
The three integrals are respectively $2\pi$, $0$ and $\pi$. Thus
$$
\boxed{\mathcal A=\frac{3\pi}{2}}
$$
in square coordinate units, agreeing with the scale-one case of the <area and perimeter of a cardioid>.