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Counting Figures - Intermediate Level: figure counting INTERMEDIATE

Master counting figures concepts through this excellence pursuit practice set. Worksheet 16 of 30 contains 20 intermediate-level problems. Deep dive into figure counting while learning shape enumeration, geometric count, visual counting. Recommended for mid-level learners aiming for moderate complexity with mixed patterns.

📝 Worksheet 16 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Intermediate level

What you'll learn in this worksheet:
Your progress through Counting Figures
Worksheet 16 of 30 (53% complete)

Question 1

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

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 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 4

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

Question 5

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 6

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

Question 7

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 8

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 9

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 10

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 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: /\ /|\ / | \ / | \ / | \ /____|____\ \ | / \ | / \ | / \ | / \|/
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 13

Count the total number of squares in the 1x1 grid below: +---+ | | +---+
In a 1x1 grid: 1 = 1
square, grid

Question 14

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

Question 15

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 16

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 17

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 18

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 19

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

Question 20

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
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