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Undoing Changes Made to Your Computer Black Screen - inBeat

📅 May 3, 2026 👤 scraface

May 03, 2026

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📌 Solution: The shortest altitude corresponds to the longest side, which is 15 m. First, compute the area of the triangle using Herons formula. The semi-perimeter $s$ is:

📌 Question: An archaeologist models the base of an ancient pillar as a regular hexagon inscribed in a circle of radius 10 m. What is the area of this hexagonal base in square meters?

📌 Solution: A regular hexagon inscribed in a circle has side length equal to the radius of the circle, so each side is 10 m. A regular hexagon can be divided into 6 equilateral triangles, each with side length 10 m. The area of one equilateral triangle is:

📌 Question: A quantum materials researcher analyzes a triangular lattice node where the sides measure 7 cm, 24 cm, and 25 cm. What is the radius of the circumscribed circle around this triangle?

📌 Solution: First, verify that the triangle is right-angled. Check:

📌 So it is a right triangle with hypotenuse 25 cm. In a right triangle, the circumradius $R$ is half the hypotenuse:

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