1. **State the problem:** Calculate the area of the shaded region inside a rectangle of length 12 m and height 7 m, with two semicircles on the left and right sides inside the rectangle, each with radius 3.5 m (half the height). 2. **Identify the shapes and formulas:** - Area of rectangle: $A_{rect} = \text{length} \times \text{height} = 12 \times 7$ - Area of a semicircle: $A_{semi} = \frac{1}{2} \pi r^2$ - The shaded area is the rectangle area minus the areas of the two semicircles (since the semicircles curve inward, the shaded region excludes them). 3. **Calculate the rectangle area:** $$A_{rect} = 12 \times 7 = 84$$ 4. **Calculate the radius of each semicircle:** $$r = \frac{7}{2} = 3.5$$ 5. **Calculate the area of one semicircle:** $$A_{semi} = \frac{1}{2} \pi (3.5)^2 = \frac{1}{2} \pi \times 12.25 = 6.125\pi$$ 6. **Calculate the total area of two semicircles:** $$2 \times 6.125\pi = 12.25\pi$$ 7. **Calculate the shaded area:** $$A_{shaded} = A_{rect} - 12.25\pi = 84 - 12.25\pi$$ 8. **Approximate the shaded area using $\pi \approx 3.1416$:** $$12.25 \times 3.1416 = 38.48$$ $$A_{shaded} \approx 84 - 38.48 = 45.52$$ **Final answer:** The area of the shaded region is approximately $45.52$ square meters.