CT 22: Reasoning (Counting Figures গণনা পরিসংখ্যান)

1) If a figure is made by intersecting 3 rectangles, each rotated 45 degrees from the previous, how many total regions are created by these intersections?

2) A star-shaped figure is created by overlapping two identical triangles. If each triangle has sides of length 6 units, how many distinct triangles can be counted within this star figure?

3) In a pattern of concentric squares with each square divided into 4 equal smaller squares, totaling 3 layers of squares, how many individual squares are present in the entire figure?

4) Given a figure with a hexagon surrounded by 6 equilateral triangles, how many unique quadrilaterals can be identified by joining the vertices of the hexagon with the vertices of the triangles?

5) Consider a figure with a large triangle divided into smaller triangles by drawing 3 lines parallel to its base. How many triangles, regardless of size, can be identified in this figure?

6) If a figure is composed of 5 overlapping squares, each sharing half of their sides with adjacent squares, how many total regions are formed within the figure?

7) In a complex diagram consisting of overlapping triangles, squares, and circles, how many distinct triangles can be identified if each triangle shares at least one side with another shape?

8) In a diagram with a circle enclosed by four rectangles, each touching the circle, how many total intersections are formed by the lines of the rectangles and the circle?

9) In a geometric figure composed of two overlapping squares and a circle intersecting both squares, how many regions are formed in the plane of the figure?

10) A complex figure consists of a combination of 4 overlapping circles of equal radii. Each pair of circles intersects exactly twice. How many distinct regions are created by these intersections?