Discussion
A square pyramid of base 40 mm side and height 50 mm has a lateral edge of about
Answer: B
The lateral edge runs from the apex to a base corner, so the horizontal distance it spans is half the base diagonal, not half the base side. For a square base of side \( a = 40 \) mm, \[ \tfrac{1}{2}d \;=\; \frac{a\sqrt{2}}{2} \;=\; \frac{40\sqrt{2}}{2} \;=\; 20\sqrt{2} \;\approx\; 28.28\ \text{mm}. \] The edge is then the hypotenuse on that and the axis height \( h = 50 \) mm: \[ l \;=\; \sqrt{h^{2} + \left(\tfrac{1}{2}d\right)^{2}} \;=\; \sqrt{50^{2} + \left(20\sqrt{2}\right)^{2}} \;=\; \sqrt{2500 + 800} \;=\; \sqrt{3300} \;\approx\; 57.4\ \text{mm}. \] Using half the base side instead gives the slant height of a face, \[ \sqrt{50^{2} + 20^{2}} \;=\; \sqrt{2900} \;\approx\; 53.9\ \text{mm}, \] which is the distractor offered at option A.
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