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Counting Figures - Expert Level: combined counting EXPERT

Intensive progress check 🎯 drill: 20 expert-level counting figures questions. Worksheet 30 of 30 hones your combined counting abilities. Practice shape enumeration, geometric count, visual counting under timed conditions. Best for expert-level students seeking challenging problems and time-bound practice.

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

What you'll learn in this worksheet:
Your progress through Counting Figures
Worksheet 30 of 30 (100% complete)

Question 1

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

Question 2

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

Question 3

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

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 triangles in the triangular grid below (2 rows): /\ /__\ /\ /\ /__\/__\
Upward pointing triangles: 4, Downward pointing triangles: 1. Total = 4 + 1 = 5
triangle, grid

Question 6

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 7

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

Question 10

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 11

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 12

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 13

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

Question 14

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 15

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 16

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

Question 17

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 18

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 19

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

Question 20

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
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