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Counting Figures - Beginner Level: figure counting BEGINNER

This foundation builder 🌟 worksheet contains 20 beginner-level counting figures problems. Worksheet 1 of 30 focuses on figure counting. Practice figure counting, shape enumeration, geometric count with our step-by-step solutions. Difficulty: foundational concepts and basic patterns. Recommended for entry-level learners.

📝 Worksheet 1 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Beginner level

What you'll learn in this worksheet:
Your progress through Counting Figures
Worksheet 1 of 30 (3% complete)

Question 1

Count the number of squares in the following figure: A 3x3 square grid with both diagonals in the center square only: +---+---+---+ | | | | +---+---+---+ | | | | +---+---+---+ | | | | +---+---+---+
Total squares in a 3x3 grid = 14 (9 small + 4 medium + 1 large). The diagonals in the center square do not create new squares, only triangles. Total remains 14.
square, diagonals

Question 2

Count the total number of squares in the 2x3 grid below: +---+---+---+ | | | | +---+---+---+ | | | | +---+---+---+
For a 2x3 grid: (2×3) + (1×2) = 8
square, rectangle

Question 3

Count the total number of squares in the 3x4 grid below: +---+---+---+---+ | | | | | +---+---+---+---+ | | | | | +---+---+---+---+ | | | | | +---+---+---+---+
For a 3x4 grid: (3×4) + (2×3) + (1×2) = 20
square, rectangle

Question 4

Count the total number of parallelograms in the grid below (3 horizontal lines × 4 vertical lines): +---+---+---+ | | | | +---+---+---+ | | | | +---+---+---+
Choose 2 horizontal lines from 3: C(3,2) = 3, Choose 2 vertical lines from 4: C(4,2) = 6. Total = 3 × 6 = 18
parallelogram, grid

Question 5

Count the total number of triangles in the triangular grid below (3 rows): /\ /__\ /\ /\ /__\/__\ /\ /\ /\ /__\/__\/__\
Upward pointing triangles: 9, Downward pointing triangles: 3. Total = 9 + 3 = 12
triangle, grid

Question 6

Count the total number of parallelograms in the grid below (4 horizontal lines × 4 vertical lines): +---+---+---+ | | | | +---+---+---+ | | | | +---+---+---+ | | | | +---+---+---+
Choose 2 horizontal lines from 4: C(4,2) = 6, Choose 2 vertical lines from 4: C(4,2) = 6. Total = 6 × 6 = 36
parallelogram, grid

Question 7

Count the number of line segments in the following figure: o-------o-------o
With 3 points on a line, number of segments = C(3,2) = 3 segments.
line, segment

Question 8

Count the total number of rectangles (including squares) in the 2x4 grid below: +---+---+---+---+ | | | | | +---+---+---+---+ | | | | | +---+---+---+---+
Number of ways to choose 2 horizontal lines = C(3,2) = 3, Number of ways to choose 2 vertical lines = C(5,2) = 10. Total = 3 × 10 = 30
rectangle, grid

Question 9

Count the number of line segments in the following figure: o-o-o-o-o
With 5 points on a line, number of segments = C(5,2) = 10 segments.
line, segment

Question 10

Count the number of circles in the following figure: ----- / \ | O | \ / -----
Two separate circles, one inside the other. Total = 2 circles.
circle, overlap

Question 11

Count the number of squares in the following figure: +---+ |\ /| | X | |/ \| +---+
The figure shows a single square with both diagonals drawn. The diagonals create 4 triangles, but no new squares. Therefore, only 1 square exists in this figure.
square, diagonals

Question 12

Count the number of triangles in the following figure: /\ / \ / \ /______\
There is exactly 1 triangle in the figure.
triangle, basic

Question 13

Count the number of squares in the following figure: +---+ |\ /| | X | |/ \| +---+
The figure shows a single square with both diagonals drawn. The diagonals create 4 triangles, but no new squares. Therefore, only 1 square exists in this figure.
square, diagonals

Question 14

Count the total number of squares in the 2x2 grid below: +---+---+ | | | +---+---+ | | | +---+---+
In a 2x2 grid: 4 + 1 = 5
square, grid

Question 15

Count the number of triangles in the following figure: * * \ / * / \ * * (A 5-pointed star with intersecting lines) Tip: Count all triangles formed by the intersecting lines. There are 5 small triangles at the points and 5 larger triangles inside.
A pentagram contains 10 triangles: 5 small triangles at the points and 5 larger triangles formed by intersecting lines.
triangle, star

Question 16

Count the number of line segments in the following figure: o-------o-------o
With 3 points on a line, number of segments = C(3,2) = 3 segments.
line, segment

Question 17

Count the number of triangles in the following figure: /\ / \ / \ /______\
There is exactly 1 triangle in the figure.
triangle, basic

Question 18

Count the total number of triangles in the triangular grid below (2 rows): /\ /__\ /\ /\ /__\/__\
Upward pointing triangles: 4, Downward pointing triangles: 1. Total = 4 + 1 = 5
triangle, grid

Question 19

Count the total number of triangles in the triangular grid below (3 rows): /\ /__\ /\ /\ /__\/__\ /\ /\ /\ /__\/__\/__\
Upward pointing triangles: 9, Downward pointing triangles: 3. Total = 9 + 3 = 12
triangle, grid

Question 20

Count the number of line segments in the following figure: o-------o-------o
With 3 points on a line, number of segments = C(3,2) = 3 segments.
line, segment
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