1. **Problem statement:** We have a net of a rectangular pyramid with a diamond shape split into four triangles by two perpendicular dashed lines. The vertical dashed line is 11 yd from center to top vertex, and the horizontal dashed line is 14 yd total, split into two 10 yd segments from center to left and right vertices. We need to find the surface area of the pyramid it forms. 2. **Understanding the shape:** The diamond represents the four triangular faces of the pyramid. The dashed lines are the heights and bases of these triangles. The vertical line (11 yd) is the height of each triangular face, and the horizontal line (14 yd) is the total base length of the diamond, split into two segments of 10 yd each from the center to the left and right vertices. 3. **Identify the base dimensions:** The base of the pyramid is rectangular. The horizontal dashed line is 14 yd total, but the problem states 10 yd segments from center to left and right vertices, which suggests the base edges are 10 yd and 14 yd. 4. **Calculate the base area:** The base is a rectangle with sides 10 yd and 14 yd. $$\text{Base area} = 10 \times 14 = 140 \text{ yd}^2$$ 5. **Calculate the area of the four triangular faces:** Each triangular face has a base and height. The diamond is split into four triangles by the dashed lines. The vertical dashed line (11 yd) is the height of each triangle. The horizontal dashed line (14 yd) is split into two 10 yd segments, so the base lengths of the triangles are 10 yd and 14 yd respectively. Since the diamond is formed by two pairs of congruent triangles, two triangles have base 10 yd and two have base 14 yd. 6. **Calculate the area of two triangles with base 10 yd:** $$\text{Area} = \frac{1}{2} \times 10 \times 11 = 55 \text{ yd}^2$$ Total for two such triangles: $$2 \times 55 = 110 \text{ yd}^2$$ 7. **Calculate the area of two triangles with base 14 yd:** $$\text{Area} = \frac{1}{2} \times 14 \times 11 = 77 \text{ yd}^2$$ Total for two such triangles: $$2 \times 77 = 154 \text{ yd}^2$$ 8. **Calculate total lateral surface area:** $$110 + 154 = 264 \text{ yd}^2$$ 9. **Calculate total surface area of the pyramid:** $$\text{Surface area} = \text{Base area} + \text{Lateral surface area} = 140 + 264 = 404 \text{ yd}^2$$ **Final answer:** The surface area of the pyramid is **404 yd\textsuperscript{2}**.