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$$ABCD$$ is a rectangle with $$E$$ and $$F$$ are midpoints of $$CD$$ and $$AB$$ respectively and $$G$$ is the mid-point of $$AF$$. The ratio of the area of $$ABCD$$ to area of $$AECG$$ is
Taking the rectangle with width $$w$$ and height $$h$$, the quadrilateral $$AECG$$ has area $$\frac{3wh}{8}$$ by the shoelace formula, while the rectangle has area $$wh$$. So the ratio is $$wh \colon \frac{3wh}{8} = 8 \colon 3$$.
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