The area of a triangle is 35 square meters, and its base is 10 meters. Find its height.
["# How to Find the Height of a Triangle When Area and Base Are Known", "Understanding the relationship between a triangle’s area, base, and height is essential for solving geometry problems efficiently—whether it's for homework, construction planning, or everyday calculations. This article explains how to calculate the height of a triangle when the area and base are given, using a real-world example.", "## The Formula That Rules Triangle Area", "The area ( A ) of a triangle is calculated using the formula:", "[\nA = \frac{1}{2} \ imes \ ext{base} \ imes \ ext{height}\n]", "In this formula, the base is one of the triangle’s sides, and the height is the perpendicular distance from the base to the opposite vertex. Rearranging this formula allows us to solve for the unknown height when the area and base are known.", "## Given Values in the Problem", "You are told:", "- Area ( A = 35 ) square meters\n- Base ( = 10 ) meters\n- Height ( h = ? )", "## Step-by-Step Calculation", "1. Start with the area formula:\n [\n A = \frac{1}{2} \ imes \ ext{base} \ imes h\n ]", "2. Plug in the known values:\n [\n 35 = \frac{1}{2} \ imes 10 \ imes h\n ]", "3. Simplify the right-hand side:\n [\n 35 = 5 \ imes h\n ]", "4. Solve for ( h ):\n [\n h = \frac{35}{5} = 7\n ]", "## Result and Interpretation", "The height of the triangle is 7 meters. This means the perpendicular distance from the base (10 meters long) to the opposite side is 7 meters. Whether you're designing a roof, planning construction, or studying math, knowing this height helps with accurate measurements and comparisons.", "## Why This Calculation Matters", "- Practical Applications: Knowledge of height helps in calculating structural loads, materials needed, and spatial dimensions.\n- Math Confidence: Mastering the triangle area formula empowers students and professionals in geometry-centered tasks.\n- Problem-Solving Skills: Learning to isolate unknown variables enhances logical thinking usable across STEM fields.", "## Final Thoughts", "Finding the height when area and base are given is a straightforward yet powerful geometry concept. By using the area formula and basic algebra, you can determine the missing dimension in any triangle—key for academic success and real-world applications. The triangle with area 35 m² and base 10 meters has a height of 7 meters—simple, accurate, and essential.", "---", "Keywords: triangle area formula, height of a triangle, solve triangle height, how to find triangle height, geometry problem solution, area = 1/2 base height, math tutorial triangle, triangle dimensions calculation."]
