The height of a regular quadrangular prism = 8√3, and the side of the base is 8cm.

| September 26, 2021 | education

The height of a regular quadrangular prism = 8√3, and the side of the base is 8cm. Find the distance between vertex A and the point of intersection of the diagonals of the DD1C1C boundary.

Since the prism is correct, there is a square at the base of the prism, and the heights of the prism are perpendicular to the sides of the base of the prism.

Consider a right-angled triangle СDС1 and, by the Pythagorean theorem, determine the length of the hypotenuse DC1.

DC1 ^ 2 = CC1 ^ 2 + CD ^ 2 = (8 * √3) ^ 2 + 8 ^ 2 = 192 + 64 = 256.

DC1 = √256 = 16 cm.

In a regular prism, the side face is perpendicular to the base, then the diagonal DC1 is perpendicular to the AD side, and therefore the triangle AOD is rectangular, since OD belongs to DC1 and is equal to half of it. DO = DC1 / 2 = 16/2 = 8 cm.

From the triangle AOD, by the Pythagorean theorem, we define the hypotenuse AO.

AO ^ 2 = DO ^ 2 + AD ^ 2 = 8 ^ 2 + 8 ^ 2 = 64 + 64 = 128.

AO = √128 = 8 * √2 cm.

Answer: AO = 8 * √2 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.