This gives a surface area of $$55 + 44 + 6 + 6 = 111$$ Since it does not, I am guessing that the common $126$ error arose in another way:Ĭompute everything except the back face correctly. It is a bit tough to guess how an error has occurred, but if one believes the last situation is possible - haphazardly adding two edge lengths, then adding the other two edge lengths, then multiplying their respective sums - then we might expect this to occur for other pairings of edge lengths. Okay - multiply them together: $9 \times 14 = 126$. But that results in two numbers, $9$ and $14$, and the final answer is supposed to be just one number. For example, adding two of the edge lengths, $4$ and $5$, for $9$ then adding the other two edge lengths, $3$ and $11$, for $14$. So, incorrect answers can arise in more than way.Īnd, as always, there is the simple possibility of altogether not knowing what to do and haphazardly combining numbers. Meanwhile, computing each rectangular face as $3 \times 11$ yields $99$, which adds with the triangular faces to (again) produce $111$. Adding on the two triangular faces yields $144$, which is the right answer - arrived at in the wrong way! For example, one might compute the base rectangle as $4 \times 11$ and mistakenly believe all three of the rectangular faces have surface area $44$, for a total of $132$. Incidentally, even an erroneous approach could produce the correct answer. In this scenario, you could then add on the triangular faces for a total of $122$, which also appears in the list. I suppose some might have multiple mistakes for example, forgetting one of the rectangular faces, and counting both of the other two as $5 \times 11$ for a total of $110$. Indeed, each of $138$, $111$, $100$, and $89$ appears in the list of incorrect responses. Omitting units, the correct answer is $144$ and the faces have surface areas of: $6$, $6$, $33$, $44$, and $55$. One quick way to guess at wrong answers is just to forget a face.
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