Problem:
In the figure, polygons , and are isosceles right triangles; , and are squares with sides of length ; and is an equilateral triangle. The figure can be folded along its edges to form a polyhedron having the polygons as faces. The volume of this polyhedron is
Answer Choices:
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Solution:
The polyhedron is a unit cube with a corner cut off. The missing corner may be viewed as a pyramid whose altitude is and whose base is an isosceles right triangle (shaded in the figure). The area of the base is . The pyramid's volume is therefore , so the polyhedron's volume is .
