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Counting Figures - Intermediate-Advanced Level: image enumeration INTERMEDIATE-ADVANCED

Ready to master counting figures? This time-bound test features 20 intermediate-advanced-level challenges. Worksheet 22 of 30 sharpens your image enumeration skills. Master figure counting, shape enumeration, geometric count through guided practice. Perfect for advanced developing test preparation.

📝 Worksheet 22 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Intermediate-advanced level

What you'll learn in this worksheet:
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Worksheet 22 of 30 (73% complete)

Question 1

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 2

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 3

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 4

Count the number of triangles in the following figure: /\ /|\ / | \ /__|__\
The median divides the triangle into 2 smaller triangles. Total = 2 triangles.
triangle, basic

Question 5

Count the total number of squares in the 3x5 grid below: +---+---+---+---+---+ | | | | | | +---+---+---+---+---+ | | | | | | +---+---+---+---+---+ | | | | | | +---+---+---+---+---+
For a 3x5 grid: (3×5) + (2×4) + (1×3) = 26
square, rectangle

Question 6

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

Question 7

Count the total number of rectangles (including squares) in the 3x3 grid below: +---+---+---+ | | | | +---+---+---+ | | | | +---+---+---+ | | | | +---+---+---+
Number of ways to choose 2 horizontal lines = C(4,2) = 6, Number of ways to choose 2 vertical lines = C(4,2) = 6. Total = 6 × 6 = 36
rectangle, grid

Question 8

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 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 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 11

Count the total number of squares in the 2x4 grid below: +---+---+---+---+ | | | | | +---+---+---+---+ | | | | | +---+---+---+---+
For a 2x4 grid: (2×4) + (1×3) = 11
square, rectangle

Question 12

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

Question 13

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 14

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 15

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 16

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 17

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 18

Count the total number of squares in the 1x1 grid below: +---+ | | +---+
In a 1x1 grid: 1 = 1
square, grid

Question 19

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 20

Count the total number of rectangles (including squares) in the 2x3 grid below: +---+---+---+ | | | | +---+---+---+ | | | | +---+---+---+
Number of ways to choose 2 horizontal lines = C(3,2) = 3, Number of ways to choose 2 vertical lines = C(4,2) = 6. Total = 3 × 6 = 18
rectangle, grid
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