ReasoningAbility.com

Counting Figures - Beginner-Intermediate Level: visual mathematics BEGINNER-INTERMEDIATE

Intensive quick response training 🎯 drill: 20 beginner-intermediate-level counting figures questions. Worksheet 10 of 30 hones your visual mathematics abilities. Practice geometric count, visual counting, figure identification under timed conditions. Best for developing students seeking building on fundamentals with moderate challenges.

📝 Worksheet 10 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Beginner-intermediate level

What you'll learn in this worksheet:
Your progress through Counting Figures
Worksheet 10 of 30 (33% complete)

Question 1

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

Question 2

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

Question 3

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

Question 4

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

Question 5

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 6

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

Question 9

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 10

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 11

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

Question 12

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 13

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 14

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 15

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

Question 16

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 17

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 18

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

Question 19

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 20

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
Previous Worksheet Next Worksheet