Given a regular quadrangular prism abcda1b1c1d1, the base area is 8, and the side edge is 6.

Given a regular quadrangular prism abcda1b1c1d1, the base area is 8, and the side edge is 6. Find the volume of the polyhedron whose vertices are the points a, b, c, d, b1.

Let’s decide on the shape that is obtained according to the condition.

By connecting all the points, we get a rectangular pyramid, with right angles at point B. Then the edge BB1 of the pyramid will be its height.

Let’s determine the volume of the resulting pyramid.

V = Sosn * h / 3.

The area of the base, according to the condition, is 8 cm2, the height of the pyramid is equal to the length of the lateral edge of the prism. BB1 = 6 cm.

V = 8 * 6/3 = 16 cm3.

Answer: The volume of a polyhedron is 16 cm3.