A triangular plot of land has a base of 40 meters and a height of 25 meters. What is the area, and what is the length of the hypotenuse if the triangle is right-angled at the base?

["Calculating Area and Hypotenuse of a Right-Angled Triangular Plot", "When planning land development, understanding the area and dimensions of a triangular plot is essential. Imagine a triangular plot of land with a base measuring 40 meters and a height of 25 meters — and the triangle is right-angled at the base. This configuration simplifies area calculation and helps estimate the hypotenuse, which is crucial for fencing, construction, or landscaping.", "### Area of the Right-Angled Triangle", "In a right-angled triangle, the area is found using the formula:", "[\n\ ext{Area} = \frac{1}{2} \ imes \ ext{base} \ imes \ ext{height}\n]", "Given:\n- Base = 40 meters\n- Height = 25 meters", "[\n\ ext{Area} = \frac{1}{2} \ imes 40 \ imes 25 = 500 \ ext{ square meters}\n]", "This means the plot covers half a hectare — a valuable detail for real estate assessments and planning.", "### Finding the Hypotenuse", "Since the triangle is right-angled at the base, the two legs extend perpendicularly from the base and height, while the hypotenuse connects the top of the right angle to the opposite vertex, forming the longest side.", "Using the Pythagorean theorem:", "[\n\ ext{Hypotenuse}^2 = \ ext{Base}^2 + \ ext{Height}^2\n]", "[\n\ ext{Hypotenuse} = \sqrt{40^2 + 25^2} = \sqrt{1600 + 625} = \sqrt{2225} \approx 47.17 \ ext{ meters}\n]", "Rounded to two decimal places, the hypotenuse measures approximately 47.17 meters.", "### Summary", "- Area: 500 square meters\n- Hypotenuse: ~47.17 meters", "For homeowners, builders, or surveyors, knowing the area and hypotenuse enables accurate cost estimation, site layout, and compliance with zoning regulations. Whether expanding a backyard garden, constructing a deck, or designing a small commercial space, this triangular plot stands ready for development with clear mathematical insights."]