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Counting Figures - Beginner Level: figure identification BEGINNER

Boost your speed and accuracy with this beginner friendly 📈 worksheet. Worksheet 5 of 30 presents 20 beginner-level counting figures problems. Focus on figure identification while practicing figure identification, shape counting, image enumeration. Difficulty: foundational concepts and basic patterns. Perfect for entry-level test takers.

📝 Worksheet 5 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Beginner level

What you'll learn in this worksheet:
Your progress through Counting Figures
Worksheet 5 of 30 (16% complete)

Question 1

Count the total number of rectangles (including squares) in the 3x4 grid below: +---+---+---+---+ | | | | | +---+---+---+---+ | | | | | +---+---+---+---+ | | | | | +---+---+---+---+
Number of ways to choose 2 horizontal lines = C(4,2) = 6, Number of ways to choose 2 vertical lines = C(5,2) = 10. Total = 6 × 10 = 60
rectangle, grid

Question 2

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 3

Count the total number of parallelograms in the grid below (3 horizontal lines × 3 vertical lines): +---+---+ | | | +---+---+ | | | +---+---+
Choose 2 horizontal lines from 3: C(3,2) = 3, Choose 2 vertical lines from 3: C(3,2) = 3. Total = 3 × 3 = 9
parallelogram, grid

Question 4

Count the total number of rectangles (including squares) in the 2x2 grid below: +---+---+ | | | +---+---+ | | | +---+---+
Number of ways to choose 2 horizontal lines = C(3,2) = 3, Number of ways to choose 2 vertical lines = C(3,2) = 3. Total = 3 × 3 = 9
rectangle, grid

Question 5

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 6

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

Question 7

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 8

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 9

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

Question 10

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 11

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 12

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 13

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

Question 14

Count the total number of squares in the 3x3 grid below: +---+---+---+ | | | | +---+---+---+ | | | | +---+---+---+ | | | | +---+---+---+
In a 3x3 grid: 9 + 4 + 1 = 14
square, grid

Question 15

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 16

Count the total number of triangles in the triangular grid below (1 row): /\ / \ / \ /______\
Upward pointing triangles: 1, Downward pointing triangles: 0. Total = 1 + 0 = 1
triangle, grid

Question 17

Count the number of circles in the following figure: ___ ___ / \ / \ | \ / | | X | | / \ | \___/ \___/
Left circle (1), Right circle (1), Overlapping region (1) → Total 3 distinct circular regions.
circle, overlap

Question 18

Count the total number of squares in the 4x4 grid below: +---+---+---+---+ | | | | | +---+---+---+---+ | | | | | +---+---+---+---+ | | | | | +---+---+---+---+ | | | | | +---+---+---+---+
In a 4x4 grid: 16 + 9 + 4 + 1 = 30
square, grid

Question 19

Count the number of triangles in the following figure: /\ /__\ /\ /\ /__\/__\ /\ /\ /\ /__\/__\/__\
In a 3-row triangular grid: Small triangles (9) + medium triangles formed by 4 small triangles (3) + large triangle (1) = 13 total.
triangle, composite

Question 20

Count the number of triangles in the following figure: /\ /|\ / | \ /__|__\
Altitude creates 2 right triangles. Total = 2 triangles.
triangle, basic
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