It is a right triangle. Use the standard area formula: \(rac{1}{2} imes 7 imes 24 = 84 ext{ cm}^2\).

["# It Is a Right Triangle: Understanding the Fundamentals with Area Calculation", "A right triangle is one of the most fundamental and widely studied shapes in geometry. Defined by having one angle equal to 90 degrees, right triangles play a crucial role in mathematics, engineering, architecture, and navigation. In this article, we explore the defining characteristics of a right triangle, emphasize its importance in real-world applications, and illustrate its area using the standard formula.", "## What Defines a Right Triangle?", "A right triangle is a triangle that contains exactly one right angle (90°). This unique property distinguishes it from other triangles such as acute or obtuse triangles. The sides forming the right angle are called the legs, while the side opposite the right angle is known as the hypotenuse — the longest side, always opposite the largest angle.", "For example, if a triangle has legs measuring 7 cm and 24 cm, the right angle lies between these two sides, and the triangle qualifies as a right triangle.", "## Calculating the Area of a Right Triangle", "One of the most straightforward ways to find the area of any triangle — including a right triangle — is using the formula:", "[\n\ ext{Area} = \frac{1}{2} \ imes \ ext{base} \ imes \ ext{height}\n]", "In a right triangle, the two legs naturally serve as the base and height because they meet at the right angle. Applying this to a triangle with leg lengths of 7 cm and 24 cm:", "[\n\ ext{Area} = \frac{1}{2} \ imes 7,\ ext{cm} \ imes 24,\ ext{cm} = \frac{1}{2} \ imes 168,\ ext{cm}^2 = 84,\ ext{cm}^2\n]", "So, the area of the right triangle is 84 square centimeters ((84,\ ext{cm}^2)). This calculation is quick and reliable thanks to the direct relationship between the legs and the base-height formula.", "## Real-World Applications of Right Triangles", "Understanding right triangles is far more than an abstract exercise. Engineers use them in structural design, architects rely on right triangles for precise measurements, and surveyors apply them to calculate distances. Common examples include:", "- Calculating roof pitch and slope\n- Determining distances across inaccessible terrain\n- Designing triangular support frames\n- Creating graphical components in computer graphics", "The area formula ( \frac{1}{2} \ imes \ ext{leg}_1 \ imes \ ext{leg}_2 ) is essential for quantifying space, cost, and material needs in these applications.", "## Conclusion", "A right triangle is not just a theoretical concept — it is a cornerstone of geometry with widespread practical implications. By leveraging the simple yet powerful formula ( \frac{1}{2} \ imes 7 \ imes 24 = 84,\ ext{cm}^2 ), we efficiently determine its area, demonstrating how basic shapes underpin much of modern design and measurement. Whether in classroom lessons or professional practice, the right triangle remains an essential and elegant element of mathematical reasoning.", "---", "Understanding geometric principles like those of the right triangle helps build a solid foundation for problem-solving across disciplines. Next time you see a right triangle, remember its definition, its area formula, and its lasting influence on the world around you."]