# In a regular quadrangular pyramid, the height is 4√3, and the dihedral angle

In a regular quadrangular pyramid, the height is 4√3, and the dihedral angle at the base is 60 degrees. find the total surface area of the pyramid.

The dihedral angle at the base is equal to the linear angle МHО = 60.

In a right-angled triangle MOH, tg60 = MO / OH.

OH = MO / tg60 = 4 * √3 / √3 = 4 cm.

Angle OMH = (90 – 60) = 30, then the length of the OH leg is equal to half the length of the hypotenuse MH, then MH = 2 * OH = 2 * 4 = 8 cm.

The OH segment is the middle line of the triangle ABC, then AB = 2 * OH = 2 * 4 = 8 cm.

Determine the area of the triangle MBC.

Smvs = MH * BC / 2 = 8 * 8/2 = 32 cm2.

Since the side faces of the pyramid are equal in size, then Sside = 4 * Smvs = 4 * 32 = 128 cm2.

Sbn = AB ^ 2 = 82 = 64 cm2.

Then Sпов = Sсн + Sbok = 64 + 128 = 192 cm2.

Answer: The surface area of the pyramid is 19 cm2. 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.