Math CentralQuandaries & Queries


Question from Sohle:

A cube has an edge of 4 cm. A triangle is formed by joining the middle point of one face of the cube to the ends of a diagonal of the opposite face . What will be the area of the triangle ?


Here is my diagram of what you described.


$P$ is the midpoint of the top face and $BC$ is a diagonal of the opposite face. The triangle in question is green. Use Pythagoras theorem to find the base of the triangle. What is its height? What is its area?


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