What is the perimeter of the section passing through the ends of three edges extending
| August 24, 2021 | education
What is the perimeter of the section passing through the ends of three edges extending from one vertex of the cube, if the edge of the cube is equal to a.
Since the figure is a cube, then all its faces are equal, the diagonals of the side faces and the bases are equal.
From the right-angled triangle ABD, by the Pythagorean theorem, we determine the length of the hypotenuse AB.
AB ^ 2 = AD ^ 2 + BD ^ 2 = a ^ 2 + a ^ 2 = 2 * a ^ 2.
AB = a * √2 cm.
BC = AC = AB = a * √2 cm.
Determine the perimeter of the section. Ravs = AB + BC + AC = 3 * a √2 cm.
Answer: The perimeter of the section is 3 * a * √2 cm.
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