ReasoningAbility.com

Counting Figures - Intermediate-Advanced Level: figure identification INTERMEDIATE-ADVANCED

Intensive strategic solving 🎯 drill: 20 intermediate-advanced-level counting figures questions. Worksheet 20 of 30 hones your figure identification abilities. Practice shape counting, image enumeration, design counting under timed conditions. Best for advanced developing students seeking advanced concepts with increasing complexity.

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

What you'll learn in this worksheet:
Your progress through Counting Figures
Worksheet 20 of 30 (66% 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 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 3

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

Question 4

Count the number of squares in the following figure: A 2x2 square grid with both diagonals in each small square: +---+---+ | | | +---+---+ | | | +---+---+
The 4 small squares (each 1x1) + 1 large square (2x2) = 5 squares. The diagonals do not create any additional squares, only triangles.
square, diagonals

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 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 7

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 8

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 9

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 10

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

Question 13

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 14

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 15

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 16

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 17

Count the number of triangles in the following figure: /\ /|\ / | \ / | \ / | \ /____|____\ \ | / \ | / \ | / \ | / \|/
The triangle has 3 cevians (lines from vertices to opposite sides). These create 6 smaller triangles within the large triangle. Total = 6 triangles.
triangle, composite

Question 18

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

Question 19

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 20

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
Previous Worksheet Next Worksheet