1. **State the problem:** We have a rectangle with bottom side length 13 and right side length 6. Two semicircles with diameter 6 are removed from the left and right sides. 2. **Identify the shape and dimensions:** The rectangle has width 13 and height 6. The semicircles are on the left and right sides, each with diameter 6, so radius $r=\frac{6}{2}=3$. 3. **Calculate the area of the rectangle:** $$\text{Area}_{\text{rectangle}} = 13 \times 6 = 78$$ 4. **Calculate the area of one semicircle:** $$\text{Area}_{\text{semicircle}} = \frac{1}{2} \pi r^2 = \frac{1}{2} \pi (3)^2 = \frac{9\pi}{2}$$ 5. **Calculate the total area removed by two semicircles:** $$2 \times \frac{9\pi}{2} = 9\pi$$ 6. **Calculate the remaining area after removing semicircles:** $$\text{Area}_{\text{remaining}} = 78 - 9\pi$$ 7. **Final answer:** $$\boxed{78 - 9\pi}$$ This is the area of the figure after removing the two semicircles from the rectangle.