1. **State the problem:** Find the area of the composite figure composed of rectangles and a quarter circle. 2. **Identify parts of the figure:** The figure consists of: - A top rectangle 4 ft wide and 8 ft tall. - A middle section with extensions 2 ft wide on each side, total width 8 ft + 2 ft + 2 ft = 12 ft, and height 4 ft. - A quarter circle at the bottom right with radius 4 ft. - A bottom left rectangle 5 ft wide and 4 ft tall. - An inner vertical segment 3 ft tall inside the bottom right area. 3. **Calculate areas of rectangles:** - Top rectangle area: $$4 \times 8 = 32$$ sq ft. - Middle rectangle area: $$12 \times 4 = 48$$ sq ft. - Bottom left rectangle area: $$5 \times 4 = 20$$ sq ft. 4. **Calculate area of quarter circle:** - Radius $$r = 4$$ ft. - Area of full circle: $$\pi r^2 = \pi \times 4^2 = 16\pi$$ sq ft. - Area of quarter circle: $$\frac{1}{4} \times 16\pi = 4\pi \approx 12.57$$ sq ft. 5. **Sum all areas:** $$32 + 48 + 20 + 12.57 = 112.57$$ sq ft. 6. **Final answer:** The area of the figure is approximately **112.57** square feet.