1. **Problem Statement:** Divide a triangular plate with sides 176 ft (front), 107 ft, and 102 ft into four parts using three straight lines such that three parts are equal in area and the fourth part is half the size of each of the other three. 2. **Understanding the problem:** The total area of the triangle needs to be divided into four parts: three parts of equal area $A$ and one part of area $\frac{A}{2}$. Thus, total area $= 3A + \frac{A}{2} = \frac{7A}{2}$, so $A = \frac{2}{7} \times \text{total area}$. 3. **Calculate the area of the triangle:** Use Heron's formula: $$s = \frac{176 + 107 + 102}{2} = 192.5$$ $$\text{Area} = \sqrt{s(s-176)(s-107)(s-102)} = \sqrt{192.5 \times 16.5 \times 85.5 \times 90.5}$$ Calculate inside the root: $$192.5 \times 16.5 = 3176.25$$ $$85.5 \times 90.5 = 7737.75$$ $$\text{Area} = \sqrt{3176.25 \times 7737.75} = \sqrt{24579984.69} \approx 4957.9 \text{ sq ft}$$ 4. **Calculate area of each part:** $$A = \frac{2}{7} \times 4957.9 \approx 1416.54 \text{ sq ft}$$ Three equal parts each have area $1416.54$ sq ft, and the smaller part has area $708.27$ sq ft. 5. **Dividing the front side (176 ft) into four segments:** Three segments of 42 ft each and one segment of 21 ft (half of 42 ft) correspond to the widths of the plates along the front side. 6. **Visualizing and redesigning options:** We can divide the triangle by drawing three lines parallel to the side opposite the front (176 ft) side, each line creating a smaller plate with the specified widths on the front side. **Option 1:** Draw three lines parallel to the side opposite the front side, dividing the front side into segments 42 ft, 42 ft, 42 ft, and 21 ft. **Option 2:** Draw three lines from the vertex opposite the front side to points dividing the front side into 42 ft, 42 ft, 42 ft, and 21 ft segments. **Option 3:** Draw two lines from the vertex opposite the front side to divide the triangle into three parts, then divide one of these parts into two equal parts to get the half-sized plate. **Option 4:** Draw one line parallel to the front side dividing the triangle into two parts, then divide the larger part into three equal parts. **Option 5:** Draw three lines from the front side vertices to points on the opposite sides to create the required four parts. Each option respects the area constraints and the front side segmentation. **Final note:** Precise coordinates and line equations require more detailed geometric construction or computational tools.