# In a regular triangular prism ABCA1B1C1, the base area is 9, and the lateral edge is 4.

**In a regular triangular prism ABCA1B1C1, the base area is 9, and the lateral edge is 4. Find the volume of the pyramid BACC1A1.**

Since the pyramid is regular, the ABC triangle is equilateral.

Let us define the side of the triangle ABC through the area of the base of the prism. Sbn = АС^2 * √3 / 4.

AC ^ 2 = 4 * Sb / √3 = 4 * 9 / √3 = 36 / √3 cm.

AC = 6 / √√3) .

The pyramid BAСС1A1 is a rectangular pyramid with the base AA1C1C, which has its height ВН.

The BH segment in an equilateral triangle ABC is its height, median and bisector, then BH = √3 * AC / 2 = √3 * 6 / √√3 / 2 = 3 * √ (√3).

Let’s define the area of the rectangle АА1С1С. S = AC * AA1 = (6 / √√3) * 4 = 24 / √√3.

Then Vpyr = S * ВН / 3 = (24 / √√3) * 3 * √√3 / 3 = 24 / √3 = 8 * √3 cm3.

Answer: The volume of the pyramid is 8 * √3 cm3.