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Counting Figures - Intermediate-Advanced Level: visual counting INTERMEDIATE-ADVANCED

Strategic expert challenge ★ for counting figures: 20 intermediate-advanced-level problems. Worksheet 19 of 30 - Focus: visual counting. Develop expertise in figure identification, shape counting, image enumeration with step-by-step solutions. Ideal for advanced developing learners targeting advanced concepts with increasing complexity.

📝 Worksheet 19 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Intermediate-advanced level

What you'll learn in this worksheet:
Your progress through Counting Figures
Worksheet 19 of 30 (63% complete)

Question 1

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 2

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 3

Count the number of triangles in the following figure: /\ /__\ /\ /\ /__\/__\
This creates 4 small congruent triangles. Total = 4 triangles.
triangle, basic

Question 4

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 5

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 6

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 7

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 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 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 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: /\ /|\ / | \ / | \ / | \ /____|____\ \ | / \ | / \ | / \ | / \|/
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 12

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

Question 13

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

Question 14

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 15

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

Question 16

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 17

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

Question 18

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 19

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

Question 20

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