3. (10 points) Divide the diagonal of rectangle $A B C D$ into 12 equal segments, and connect them as shown in the figure. The total area of the blank parts inside rectangle $A B C D$ is 10 square centimeters. Therefore, the total area of the shaded parts is ( ) square centimeters.
A. 14
B. 16
C. 18
D. 20
【Analysis】Assuming the area of the smallest blank rectangle in the middle is taken as the unit $1=a b$, then the area of the adjacent shaded part is $2 a \times 2 b-a b=3 a b=3$. Similarly, the area of the adjacent blank part is $5 a b=5$. Following this pattern, the areas are $7, 9, 11$ respectively. Therefore, the total area of the blank parts is $1+5+9=15$. Given that the actual total area of the blank parts is 10 square centimeters, the actual area of unit 1 is $10 \div 15=\frac{2}{3}$ (square centimeters); Similarly, the total area of the shaded parts is: $3+7+11=21$, and then further solving can be done.

【Solution】Solution: Assuming the area of the smallest blank rectangle in the middle is taken as the unit $1=a b$, then the area of the adjacent shaded part is $2 a \times 2 b-a b=3 a b=3$. Similarly, the area of the adjacent blank part is $5 a b=5$. Following this pattern, the areas are $7, 9, 11$ respectively. Therefore, the total area of the blank parts is $1+5+9=15$. Given that the actual total area of the blank parts is 10 square centimeters, the actual area of unit 1 is $10 \div 15=\frac{2}{3}$ (square centimeters);

The total area of the shaded parts is: $3+7+11=21$, so the actual area is: $21 \times \frac{2}{3}=14$ (square centimeters); Answer: The total area of the shaded parts is 14 square centimeters. Therefore, the correct choice is: $A$.