1. **Stating the problem:** We have a trapezoid with a height of $2.5$ yards and the two non-parallel sides each measuring $1$ yard. We want to understand or calculate properties related to this trapezoid. 2. **Understanding the trapezoid:** A trapezoid has two parallel sides (bases) and two non-parallel sides (legs). Here, the legs are each $1$ yard, and the height (the perpendicular distance between the bases) is $2.5$ yards. 3. **Using the Pythagorean theorem:** To find the length of the bases or other properties, we can use the Pythagorean theorem if we know the horizontal distances. The legs and height form right triangles with the bases. 4. **Formula for the area of a trapezoid:** $$\text{Area} = \frac{(b_1 + b_2)}{2} \times h$$ where $b_1$ and $b_2$ are the lengths of the two bases and $h$ is the height. 5. **If the bases are unknown, and only legs and height are given, we can find the horizontal component of the legs:** $$\text{horizontal leg} = \sqrt{1^2 - 2.5^2}$$ Since $1^2 - 2.5^2 = 1 - 6.25 = -5.25$, which is negative, this means the legs cannot be $1$ yard if the height is $2.5$ yards (the legs are too short to reach that height). This suggests a possible error or that the trapezoid is not drawn to scale. 6. **Conclusion:** Given the height $2.5$ yards and legs $1$ yard, the trapezoid cannot exist as described because the legs are shorter than the height. If you want to calculate area or other properties, please provide the lengths of the bases or clarify the dimensions.