Problem: suppose you have three identical prisms with congruent equilateral triangles as the end - polygons . suppose you attach them by the rectangular faces so they are perfectly aligned . there will be some large faces created by two or more co - planar faces of the individual prisms : count each such large face as one . given that , how many faces does the resultant solid have ?
Rationale: the top and the bottom are each single faces formed by three equilateral triangles joining , as in the diagram on the left , to make an isosceles trapezoid . top = 1 face , and bottom = 1 face . this is a four - sided figure , so there are four rectangles extending from the bottom of this prism to the congruent figure at the top . notice , in particular , the larger vertical face in the “ back ” of the diagram to the right is formed by two faces of the original triangular prisms lying next to each other and smoothly joining . total = 1 top + 1 bottom + 4 sides = 6 faces . answer = b .
annotated_formula: add(add(const_4, const_1), const_1)