Given a cube whose edge is 2 cm. Find the area of the diagonal section.
| May 30, 2021 | education
For a cube, the pancakes of all edges are equal, then all the faces of the cube are squares with a side of 2 cm.
The diagonal section of the cube is a rectangle АА1С1С with two sides of the cube edge, and the other two diagonals of the square at the base of the cube.
In a right-angled triangle ACD, according to the Pythagorean theorem, AC ^ 2 = AD ^ 2 + CD ^ 2 = 4 + 4 = 8.
AC = 2 * √2 cm.
Determine the area of the diagonal section.
Sаа1с1с = АС * АА1 = 2 * √2 * 2 = 4 * √2 cm2.
Answer: The area of the diagonal section of the cube is 4 * √2 cm2.
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