Question

A regular dodecagon (12-sided regular polygon) is inscribed in a circle of radius \( r \) cm as shown in the figure. The side of the dodecagon is \( d \) cm. All the triangles (numbered 1 to 12 in the figure) are used to form squares of side \( r \) 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:
\includegraphics[width=0.5\linewidth]{8.png}

• A. 3; 4
• B. 4; 3
• C. 3; 3
• D. 3; 2

Hint:

In geometry problems involving regular polygons and inscribed shapes, carefully examine the symmetry and properties of the polygon to understand how to derive relationships for constructing new shapes.

Answer 1

The Correct Option is A

We are given a regular dodecagon inscribed in a circle, and we need to form squares using the triangles formed by connecting the center of the circle to the vertices of the dodecagon. There are 12 triangles in total, each corresponding to a side of the dodecagon. The number of squares that can be formed is 3, and each square requires 4 triangles. Hence, the correct number of squares and the number of triangles required to form each square are 3 and 4, respectively.