Different cut-outs, the same perimeter
8 written marks
Two designs start from squares of side \(12\) cm. Design A removes a quadrant of radius \(12\) cm centred at one corner. Design B removes two quadrants, each of radius \(6\) cm, centred at opposite corners. The two removed quadrants in B do not overlap.
Part a · 3 marks
Find the remaining area and outside perimeter for Design A.
Part b · 3 marks
Find the remaining area and outside perimeter for Design B.
Part c · 2 marks
Compare the designs. State the area difference and explain why equal remaining perimeters need not give equal remaining areas.
Complete-answer checking, worked solutions and indicative written criteria.
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