In a right triangle, one leg is 12 cm and the hypotenuse is 20 cm. What is the area of the triangle?
["How to Calculate the Area of a Right Triangle When One Leg and the Hypotenuse Are Known", "When solving geometry problems, understanding how to use the given measurements to find key properties like area is essential. One common scenario involves a right triangle where you know the length of one leg and the hypotenuse—especially when calculating the area. In this article, we’ll explore how to determine the area of a right triangle with one leg measuring 12 cm and the hypotenuse measuring 20 cm.", "---", "### Understanding the Right Triangle Properties", "In a right triangle, the three sides relate via the Pythagorean theorem:\n[\na^2 + b^2 = c^2\n]\nwhere ( c ) is the hypotenuse, and ( a ) and ( b ) are the legs.", "Here:\n- One leg ( a = 12 ) cm\n- Hypotenuse ( c = 20 ) cm\n- The other leg ( b ) is unknown", "Using the Pythagorean theorem, we can find the missing leg:", "[\n12^2 + b^2 = 20^2\n]\n[\n144 + b^2 = 400\n]\n[\nb^2 = 400 - 144 = 256\n]\n[\nb = \sqrt{256} = 16 \ ext{ cm}\n]", "---", "### Calculating the Area", "The area ( A ) of a right triangle is given by:\n[\nA = \frac{1}{2} \ imes \ ext{leg}_1 \ imes \ ext{leg}_2\n]\nSubstituting the two known legs:\n[\nA = \frac{1}{2} \ imes 12 \ imes 16 = \frac{1}{2} \ imes 192 = 96 \ ext{ cm}^2\n]", "---", "### Why This Matters in Real-World Applications", "Understanding how to calculate area from leg and hypotenuse measurements is valuable in architecture, construction, and design—areas where triangular frame components are common. The formula ensures efficient planning and accurate material estimation.", "---", "### Summary", "- Given: one leg = 12 cm, hypotenuse = 20 cm\n- Found the other leg = 16 cm via Pythagorean theorem\n- Area = ( \frac{1}{2} \ imes 12 \ imes 16 = 96 \ ext{ cm}^2 )", "By applying basic geometric principles, even complex triangle problems become manageable. Knowing how to extract unknown sides and apply area formulas empowers better mathematical and practical decision-making.", "---", "Keywords: right triangle area, how to find area given leg and hypotenuse, Pythagorean theorem, right triangle with 12 cm leg and 20 cm hypotenuse, triangle area calculation, geometry problems, math tutorial, right triangle properties."]
