3. (8 points) Four identical circular arcs form the floor tile shown in figure (1), and each arc is a quarter of the same circle (such floor tiles can tessellate the plane as shown in figure (2)). If the distance between the midpoints of two adjacent outward convex arcs is 30 cm, then the area of one floor tile is $\qquad$ square centimeters.
【Answer】 450
Solution:
$$
\begin{array}{l}
30 \div 2=15 \text { (cm) } \\
3.14 \times(30 \div 2)^{2} \div 4-15 \times 15 \div 2 \\
=3.14 \times 225 \div 4-112.5 \\
=176.625-112.5 \\
=64.125 \text { (square cm) } \\
3.14 \times(30 \div 2)^{2}-64.125 \times 4 \\
=3.14 \times 225-256.5 \\
=706.5 \text { - } 256.5 \\
=450 \text { (square cm) }
\end{array}
$$

Answer: The area of a floor tile is 450 square cm.
Therefore, the answer is: 450.