GATE DA 2025 Set 1 — Question 8
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General Aptitude → Quantitative Aptitude → 2D & 3D Patterns
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Question
A regular dodecagon (12-sided regular polygon) is inscribed in a circle of radius cm as shown in the figure. The side of the dodecagon is cm. All the triangles (numbered 1 to 12) in the figure are used to form squares of side cm and each numbered triangle is used only once to form a square.The number of squares that can be formed and the number of triangles required to form each square, respectively, are:Note: The figure shown is representative.
Correct answer
(A) 3; 4
Solution
A regular dodecagon consists of 12 congruent isosceles triangles meeting at the center. The central angle of each triangle is . The two equal sides are the radius .
The area of one such triangle is given by:The total area of the 12 triangles is:We want to form squares of side . The area of one such square is .
The number of squares that can be formed is:The number of triangles required to form one square is:Thus, 3 squares can be formed, and 4 triangles are required for each square.
The area of one such triangle is given by:The total area of the 12 triangles is:We want to form squares of side . The area of one such square is .
The number of squares that can be formed is:The number of triangles required to form one square is:Thus, 3 squares can be formed, and 4 triangles are required for each square.
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