Inscribed polygons

Geometry Level 3

A circle is inscribed in a regular octagon of side 10 10 . Next, a regular pentagon is inscribed in this circle. Next, a circle is inscribed in this pentagon. Next, a square is inscribed in this circle. Next, a circle is inscribed in this square. Find the area of the smallest circle rounded to the nearest integer. Use 22 7 \dfrac{22}{7} as an approximation for π \pi .

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