2026 · Q59
A square of side length 4 cm has its corners cut away in such a manner so as to form a regular octagon. What is the length of the side of the octagon? (Take √2 = 1.41)
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A1.00 cm
- B1.64 cm
- C1.68 cm
- D1.72 cm
Explanation
Cutting right-isosceles corner triangles of leg t leaves octagon side s = t√2 and the remaining middle of each square side 4 − 2t = s. Hence 4 − s√2 = s, i.e. s(1 + √2) = 4, so s = 4/2.41 ≈ 1.66 cm with √2 = 1.41. The nearest option is 1.64 cm, option B.