Question 1

How many squares are there in a 3×3 grid (a grid with 3 rows and 3 columns of small squares)?

Accepted Answer

In a 3×3 grid: 9 squares of size 1×1, plus 4 squares of size 2×2, plus 1 square of size 3×3 = 14 squares total.

Question 2

In a complex figure, there are 4 large squares arranged in a 2×2 grid. Inside each large square, there are 3 smaller squares arranged horizontally. Additionally, there are 2 diagonal lines drawn from the top-left corner of the entire grid to the bottom-right corner of the entire grid, and 2 more diagonal lines drawn from top-right to bottom-left. How many total squares of all sizes can be counted in this figure?

Accepted Answer

This question tests the ability to count overlapping squares of multiple sizes while accounting for squares formed by intersecting lines.

Question 3

A figure consists of a rectangle divided into 6 equal parts by 2 horizontal and 2 vertical lines (creating a 3×2 grid of rectangles). Additionally, there are 3 diagonal lines: one from top-left to bottom-right of the entire figure, one from top-right to bottom-left, and one horizontal line through the exact middle of the figure. How many triangles of all sizes are formed in this figure?

Accepted Answer

This question requires counting triangles formed by the intersection of multiple lines in a rectangular grid.

Question 4

A figure shows a hexagon with all 6 vertices connected to the center point, creating 6 triangular sections. Additionally, each of the 6 outer edges of the hexagon is divided into 2 equal parts by a point, and each of these 6 points is connected to the center. How many triangles of all sizes exist in the final figure?

Accepted Answer

This question tests counting triangles in a radial figure with multiple layers of subdivision.

Question 5

A square is divided by 3 horizontal and 3 vertical lines into a 4×4 grid of 16 small squares. Additionally, one diagonal line is drawn from the top-left corner to the bottom-right corner. How many quadrilaterals (including squares and rectangles) of all sizes can be counted in this figure?

Accepted Answer

This question requires counting all quadrilaterals in a grid with one diagonal, which creates complex overlapping regions.

Question 6

A figure consists of 3 concentric circles with 4 radii drawn from the center to the outer circle, dividing the circles into 4 equal sectors. Additionally, 2 chords are drawn connecting non-adjacent points on the outer circle. How many regions (including triangular and non-triangular) are created in this figure?

Accepted Answer

This question tests counting regions formed by circles, radii, and chords with multiple intersection points.

Question 7

A rectangle is divided by 2 horizontal lines and 3 vertical lines into a 3×4 grid. A diagonal line is drawn from one corner to the opposite corner, and a second diagonal line is drawn from another corner to its opposite corner (forming an X). How many triangles are formed by these lines?

Accepted Answer

This question requires counting triangles formed by grid lines and two intersecting diagonals.

SSC GD Constable Counting Figures

Counting Figures— Rules & Concept

Key Points to Remember

Exam-Specific Tips

Counting Figures — Practice Questions

60-Second Revision — Counting Figures