# In a regular four-pointed prism, the sides are 12 cm and 6 cm: the area

In a regular four-pointed prism, the sides are 12 cm and 6 cm: the area of its lateral surface is half the area of the full surface, calculate the height of the pyramid

Determine the area of the base of the prism.

Sbn = AB * AC = 6 * 12 = 72 cm2.

The total surface area of the prism is:

Sпов = 2 * Sсн + S side. (1)

By condition, Sbok = Sпов / 2, then Sпов = 2 * Sbok.

Substitute in equation 1.

2 * S side = 2 * S main + S side.

Side = 2 * Sb = 2 * 72 = 144 cm2.

Sbok = Ravsd * AA1, where Ravsd is the base perimeter.

144 = 2 * (12 + 6) * AA1.

AA1 = 144/36 = 4 cm.

Answer: The height of the prism is 4 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.