In the rectangular parallelepiped ABCDA1B1C1D1, the lengths of the edges are known: AB = 4, AD = 6

| September 24, 2021 | education

In the rectangular parallelepiped ABCDA1B1C1D1, the lengths of the edges are known: AB = 4, AD = 6, AA1 = 12. Find the distance from vertex A to the center of face BCC1B1.

Since the parallelepiped is straight, its bases and side faces are rectangles.

Then in a right-angled triangle BC1C, by the Pythagorean theorem, we determine the length of the hypotenuse BC1.

BC1 ^ 2 = BC ^ 2 + CC1 ^ 2 = 36 + 144 = 180.

BC1 = 6 * √5 cm.

The diagonals of the rectangle are divided in half at the point of intersection, then VO = BC1 / 2 = 6 * √5 / 2 = 3 * √5 cm.

The ABO triangle is rectangular, since the side faces of АА1В1В and ВВ1С1С are perpendicular. Then, by the Pythagorean theorem, AO ^ 2 = BO ^ 2 + AB ^ 2 = 45 + 15 = 60.

AO = √60 = 2 * √15 cm.

Answer: From point A to the center of the face BCC1B1 2 * √15 cm.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.