Discussion
Which of the following has its area and perimeter numerically equal?
Answer: C
Compare each shape's area with its perimeter.
- Equilateral triangle, side 1: area \( \tfrac{\sqrt{3}}{4} = 0.43 \), perimeter 3
- Square, side 1: area 1, perimeter 4
- Regular pentagon, side 1: area 1.72, perimeter 5
- Square, side 4: area \( 4^{2} = 16 \), perimeter \( 4 \times 4 = 16 \) ✓
Only the square of side 4 cm has the two numerically equal. For a square, \( a^{2} = 4a \) forces \( a = 4 \) - a single size, and the reason unit-sided shapes cannot work.
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