ÁREA DE UN CUADRADO INSCRITO EN UNA SEMICIRCUNFERENCIA

ÁREA DE UN CUADRADO INSCRITO EN UNA SEMICIRCUNFERENCIA

by Matemáticas con Juan

Formal & Physical Sciences Mathematics PBMGeometryPBMHEuclidean geometry
🎙 Matemáticas con Juan 👥 2.1M 📅 July 23, 2026 ⏱ 15 min 👁 8K 📄 tutorial 🧭 2026-08-06
Available in: English (current) Français

Keywords

cuadrado inscritosemicircunferenciateorema de Pitágorasecuación de segundo gradoárea

Summary

The video solves a geometry problem: finding the area of a square inscribed in a semicircle, given that the two segments outside the square on the diameter are each 3 cm. The creator parametrizes the side of the square as 2x, making the half-side x. He identifies a right triangle with legs x and 2x, and hypotenuse equal to the radius, expressed as x+3. Applying the Pythagorean theorem yields the equation (x+3)^2 = x^2 + (2x)^2, which simplifies to 4x^2 - 6x - 9 = 0. Solving this quadratic using the quadratic formula gives x = 3/4(1+√5). Since the side of the square is 2x, its area is (2x)^2 = 4x^2, which simplifies to 9/2(3+√5) cm². The video covers parametrization, Pythagorean theorem, binomial expansion, radicals, and solving quadratic equations. It concludes with a proposed problem for viewers to practice.

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Critical Evaluation

The video provides a clear and rigorous step-by-step solution to a classic geometry problem. The mathematical reasoning is sound: the parametrization of the square’s side as 2x simplifies the calculations, and the identification of the right triangle is correct. The application of the Pythagorean theorem is accurate, leading to a quadratic equation that is solved correctly using the quadratic formula. The simplification of the radical and the final expression for the area are properly handled. The creator’s teaching style is engaging, with occasional humorous asides, which makes the content accessible. However, the video does not cite any external sources, which is typical for a tutorial of this nature. The explanation is thorough, but some steps, such as the simplification of the radical, could be explained in more detail for beginners. Overall, the video is a valuable resource for students learning geometry and algebra, providing a worked example that integrates multiple concepts. The adéquation between title and content is perfect. The video’s quality is high, with clear audio and visual aids, though the creator mentions recording in a ‘dangerous place’ due to noise, which does not affect the content. The proposed problem at the end encourages active learning. In summary, this is a well-executed educational video that effectively teaches problem-solving skills.

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Title / Content Match

The title accurately describes the content: calculating the area of a square inscribed in a semicircle.

Quality & Reliability

8/10

The video presents a clear, step-by-step geometric solution using the Pythagorean theorem and quadratic equations. The reasoning is mathematically sound, and the final answer is correct. The creator is experienced and provides a thorough explanation, though no external sources are cited.

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Contribution & Novelties

The video offers a clear, step-by-step solution to a classic geometry problem, emphasizing the importance of parametrization and the application of the Pythagorean theorem to derive a quadratic equation. It demonstrates how to transform a geometric figure into an algebraic problem, a key skill in mathematics.

Pour aller plus loin :

  • Pythagorean theorem — Fundamental relation in geometry used here.
  • Quadratic formula — Method used to solve the derived equation.
  • Inscribed square — General concept of a square inscribed in a circle or semicircle.

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Radar Profile

The radar profile shows high scores in quality and reliability, with moderate scores in quantity and technical level, indicating a focused, well-explained tutorial without extensive extra content.

Reliability 8/10