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

This deep dive ★ worksheet contains 20 beginner-intermediate-level counting figures problems. Worksheet 11 of 30 focuses on triangle counting. Practice visual counting, figure identification, shape counting with our step-by-step solutions. Difficulty: building on fundamentals with moderate challenges. Recommended for developing learners.

📝 Worksheet 11 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Beginner-intermediate level

What you'll learn in this worksheet:
Your progress through Counting Figures
Worksheet 11 of 30 (36% 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: 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 3

Count the number of triangles in the following figure: /\ / \ / \ /______\
There is exactly 1 triangle in the figure.
triangle, basic

Question 4

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 5

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

Question 6

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 7

Count the number of line segments in the following figure: +---+ |\ /| | X | |/ \| +---+
Square has 4 sides + 2 diagonals = 6. Plus the segments created by diagonal intersection? Actually, each diagonal is split into 2 segments, giving 4 more. Total = 8 line segments.
line, segment

Question 8

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 9

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

Question 10

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 11

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 12

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 13

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 14

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 15

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 16

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

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 3x4 grid below: +---+---+---+---+ | | | | | +---+---+---+---+ | | | | | +---+---+---+---+ | | | | | +---+---+---+---+
For a 3x4 grid: (3×4) + (2×3) + (1×2) = 20
square, rectangle

Question 19

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 20

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