Cut a corner off and the perimeter does not change
A surprising compound-shape result: cutting corners from a rectangle changes the area but not the perimeter.
The Question
A rectangle measures 12 cm by 8 cm. A 3 cm square is cut from each of two opposite corners. Find the area and the perimeter of the shape that remains.
The Answer
Reveal the Answer
Area: 96 − 2 × 9 = 78 cm². Perimeter is the surprise — removing a corner square swaps two outer edges for two inner ones of the same total length, so it stays at 40 cm. A genuinely memorable result.
Now watch the solution
Practice Sheet + Marked Answers
The four-question practice sheet, the solutions in our teaching voice and a self-marking quiz for this question are part of The Question Desk course — every school day of the term, with progress you can see. Enrolled group students get it included.
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