ReasoningAbility.com

Counting Figures - Beginner-Intermediate Level: square counting BEGINNER-INTERMEDIATE

Ready to master counting figures? This benchmark test features 20 beginner-intermediate-level challenges. Worksheet 12 of 30 sharpens your square counting skills. Master figure identification, shape counting, image enumeration through guided practice. Perfect for developing test preparation.

📝 Worksheet 12 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Beginner-intermediate level

What you'll learn in this worksheet:
Your progress through Counting Figures
Worksheet 12 of 30 (40% complete)

Question 1

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 2

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 3

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 4

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 5

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 6

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 7

Count the number of triangles in the following figure: Triangular grid with 4 rows
In a 4-row triangular grid: Small triangles (16) + medium triangles of size 2 (7) + medium triangles of size 3 (3) + large triangle (1) = 27 total.
triangle, composite

Question 8

Count the number of triangles in the following figure: Triangular grid with 4 rows
In a 4-row triangular grid: Small triangles (16) + medium triangles of size 2 (7) + medium triangles of size 3 (3) + large triangle (1) = 27 total.
triangle, composite

Question 9

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 10

Count the number of circles in the following figure: --------- / \ | ----- | | / \ | | | O | | | \ / | | ----- | \ / ---------
Three separate circles, one inside the other. Total = 3 circles.
circle, overlap

Question 11

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 12

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 13

Count the number of triangles in the following figure: Triangular grid with 4 rows
In a 4-row triangular grid: Small triangles (16) + medium triangles of size 2 (7) + medium triangles of size 3 (3) + large triangle (1) = 27 total.
triangle, composite

Question 14

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 15

Count the number of line segments in the following figure: o---o---o---o
With 4 points on a line, number of segments = C(4,2) = 6 segments.
line, segment

Question 16

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 17

Count the number of triangles in the following figure: Triangular grid with 4 rows
In a 4-row triangular grid: Small triangles (16) + medium triangles of size 2 (7) + medium triangles of size 3 (3) + large triangle (1) = 27 total.
triangle, composite

Question 18

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

Question 19

Count the number of circles in the following figure: --------- / \ | ----- | | / \ | | | O | | | \ / | | ----- | \ / ---------
Three separate circles, one inside the other. Total = 3 circles.
circle, overlap

Question 20

Count the number of triangles in the following figure: /\ / \ / \ / \ / \ / \ \ / \ / \ / \ / \ / \/ (A 6-pointed star formed by two overlapping triangles) Tip: Count all triangles - 6 small at the points + 2 large overlapping = 8 triangles.
A hexagram contains 8 triangles: 6 small triangles at the points and 2 large overlapping triangles.
triangle, star
Previous Worksheet Next Worksheet