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A
A circle
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B
A six-sided shape (hexagon) if the triangle adds one new edge to each side it doesn't share with the pentagon — but the exact shape depends on the triangle's geometry; the goal is to imagine the contour of the combined figure
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C
Another pentagon
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D
Two separate shapes
Why this is the answer
When two pieces share a complete edge (the edges match in length and orientation), the SHARED EDGE DISAPPEARS in the combined shape, and the contour follows the NON-SHARED EDGES of both pieces. EXAMPLE: a pentagon has 5 sides; a triangle has 3 sides; if the triangle attaches its base to one side of the pentagon, the shared edge becomes internal; the combined shape's contour follows the remaining 4 sides of the pentagon plus the remaining 2 sides of the triangle = 6 edges total (a hexagon, though typically irregular). RULES for visualizing combined shapes: (1) IDENTIFY the SHARED EDGE — it must match exactly in length on both pieces; (2) The shared edge is INTERIOR to the combined shape — it's no longer on the contour; (3) The CONTOUR follows the perimeter of one piece, around to where the shared edge meets the other piece, then follows the perimeter of the other piece, back to where the shared edge meets the first piece; (4) COUNT TOTAL EDGES: (edges of piece 1) + (edges of piece 2) - 2 = total edges in combined shape (we subtract 2 because both pieces lose one edge each — the shared edge); (5) Look at how the CORNERS line up at the shared edge — if the corners are different angles, the combined shape may have new shapes near those corners. PRACTICAL FOR AO: when looking at answer choices, identify what the combined contour MUST look like based on the pieces given. If a piece has a notch (concave angle), the combined shape may also have a notch (unless the notch is filled by another piece). If a piece has a sharp 30° angle, the combined shape may have that sharp angle (or it could be at the interior shared edge and hidden). Pattern recognition: experienced AO test-takers learn to recognize common piece combinations. A square + right triangle = pentagon or rectangle (depending on orientation). Two right triangles = square or rectangle (if hypotenuses match). Two pentagons = various shapes. PRACTICE: cut paper shapes and combine them physically; this builds the mental library of combined shapes.
Source: ASVAB AO, Combining Shapes