/sci/ - Science & Math

Need some verification on this meme problem.
Graphed on Desmos: https://www.desmos.com/calculator/qevzqjrg4k
Pretty much what I did was split the yellow area into 2 areas where the lower function would change form [math]y=1/2(1-2(-x^{2}-x)^{.5})[/math] to [math]y=\sqrt{1-x^{2}}[/math] at [math]x=-\frac{5}{8}-\frac{\sqrt{7}}{8}[/math] and did the usual integration business of [math]A_{intersect}=\int _a^bf(x)dx-\int _a^bg(x)dx[/math] where [math]f(x)>g(x), x\in[a,b][/math].
The smaller area being
[math]A_{small}=\int _{-1}^{-\frac{5}{8}-\frac{\sqrt{7}}{8}} 1/2(2(-x^2-x)^{.5}+1)dx -\int _{-1}^{-\frac{5}{8}-\frac{\sqrt{7}}{8}}1/2(1-2(-x^2-x)^{.5})dx\approx 0.012257759872[/math]
The bigger being
[math]A_{larger}=\int_{-\frac{5}{8}-\frac{\sqrt{7}}{8}}^{\sqrt7/8 - 5/8}1/2(2(-x^2-x)^{.5}+1)dx-\int_{-\frac{5}{8}-\frac{\sqrt{7}}{8}}^{\sqrt7/8 - 5/8}\sqrt{1-x^{2}}dx\approx 0.134123499657[/math]
Total gives [math]0.146381259530[/math]

Is there a way to do this problem purely from a geometric standpoint using only the area formulas for a square and circle?