A rectangle of certain dimensions is chopped off from one corner of a larger rectangle as shown. $AB = 8$ cm and $BC = 4$ cm. The perimeter of the figure $ABCPQRA$ (in cm) is

### Concept & Geometric Transformation When a rectangular corner is removed from a larger rectangle, the perimeter of the resulting shape remains exactly the same as the original un-chopped rectangle. ### Step-by-Step Solution * The total perimeter of the figure is the sum of its outer boundary: $AB + BC + CP + PQ + QR + RA$. * Notice the horizontal segments: The sum of the chopped horizontal segment $CP$ and the inner horizontal segment $QR$ is exactly equal to the full bottom length $AB$. $$ CP + QR = AB = 8 \text{ cm} $$ * Notice the vertical segments: The sum of the inner vertical segment $PQ$ and the chopped vertical segment $RA$ is exactly equal to the full right-side length $BC$. $$ PQ + RA = BC = 4 \text{ cm} $$ * Now, substitute these sums into the perimeter equation: $$ \text{Perimeter} = AB + BC + (CP + QR) + (PQ + RA) $$ $$ \text{Perimeter} = 8 + 4 + 8 + 4 $$ $$ \text{Perimeter} = 24 \text{ cm} $$ ### Exam Strategy & Shortcut Visualize "pushing" the inner line segments $PQ$ and $QR$ outward to fill the gap. $PQ$ slides right to complete the right edge, and $QR$ slides up to complete the top edge. The shape becomes a perfect $8 \times 4$ rectangle. Perimeter = $2(8 + 4) = 24$. ### Common Pitfall Assuming that removing area must also reduce the perimeter, leading test-takers to guess lower numbers without analyzing the lengths of the new edges created by the cut. ### Final Answer Therefore, the correct answer is **24**.