A triangle has sides of length 7 cm, 24 cm, and 25 cm. What is the area of the triangle in square centimeters?
["Title: How to Calculate the Area of a Triangle with Sides 7 cm, 24 cm, and 25 cm – A Step-by-Step Guide", "When given a triangle with side lengths of 7 cm, 24 cm, and 25 cm, understanding its area is a fundamental geometry problem that many students and math enthusiasts encounter. Interesting enough, this triangle is not just any triangle—it’s a right triangle, which makes calculating its area both straightforward and insightful.", "### Understanding the Triangle’s Shape", "Before diving into calculations, it’s essential to recognize the type of triangle we’re dealing with. Notice that:", "[\n7^2 + 24^2 = 49 + 576 = 625\n]\n[\n25^2 = 625\n]", "Since (7^2 + 24^2 = 25^2), this confirms the triangle is a right-angled triangle with legs measuring 7 cm and 24 cm, and the hypotenuse measuring 25 cm.", "### Calculating the Area of a Right Triangle", "For any right triangle, the area is calculated using the formula:", "[\n\ ext{Area} = \frac{1}{2} \ imes \ ext{base} \ imes \ ext{height}\n]", "Here, the two legs (7 cm and 24 cm) serve as the base and height:", "[\n\ ext{Area} = \frac{1}{2} \ imes 7 \ imes 24\n]", "First, multiply:", "[\n7 \ imes 24 = 168\n]", "Then divide by 2:", "[\n\ ext{Area} = \frac{168}{2} = 84\n]", "### Final Result", "Thus, the area of the triangle with sides 7 cm, 24 cm, and 25 cm is:", "[\n\boxed{84 \ ext{ cm}^2}\n]", "This simple right triangle reminds us how powerful geometric principles can be—especially when identifying special triangles like the 7-24-25 Pythagorean triple, which retains relatable real-world applications and elegant mathematical properties.", "### Why This Matters", "Knowing how to compute the area of triangles is crucial not just for academic success but also for fields like architecture, engineering, and design. The 7-24-25 triangle is favorite in practical problem-solving due to its clean right-angle geometry and integer side lengths, making it a classic example in teaching triangles, trigonometry, and the Pythagorean theorem.", "So next time you see these side lengths, remember: it’s a right triangle with a comfortable, computable area of 84 cm²—no complex formulas required!"]
