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Counting Figures - Intermediate Level: shape enumeration INTERMEDIATE

Quick mental agility ★ session: 20 intermediate-level counting figures questions. Worksheet 17 of 30 - Focus: shape enumeration. Practice geometric count, visual counting, figure identification with instant feedback. Great for mid-level students needing moderate complexity with mixed patterns practice.

📝 Worksheet 17 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Intermediate level

What you'll learn in this worksheet:
Your progress through Counting Figures
Worksheet 17 of 30 (56% complete)

Question 1

Count the total number of rectangles (including squares) in the 2x2 grid below: +---+---+ | | | +---+---+ | | | +---+---+
Number of ways to choose 2 horizontal lines = C(3,2) = 3, Number of ways to choose 2 vertical lines = C(3,2) = 3. Total = 3 × 3 = 9
rectangle, grid

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 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 4

Count the total number of triangles in the triangular grid below (1 row): /\ / \ / \ /______\
Upward pointing triangles: 1, Downward pointing triangles: 0. Total = 1 + 0 = 1
triangle, grid

Question 5

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

Question 6

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 7

Count the total number of rectangles (including squares) in the 2x2 grid below: +---+---+ | | | +---+---+ | | | +---+---+
Number of ways to choose 2 horizontal lines = C(3,2) = 3, Number of ways to choose 2 vertical lines = C(3,2) = 3. Total = 3 × 3 = 9
rectangle, grid

Question 8

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 9

Count the number of triangles in the following figure: /\ /|\ / | \ /__|__\
Altitude creates 2 right triangles. Total = 2 triangles.
triangle, basic

Question 10

Count the number of triangles in the following figure: /\ /|\ / | \ /__|__\
Altitude creates 2 right triangles. Total = 2 triangles.
triangle, basic

Question 11

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 12

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 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 circles in the following figure: ___ ___ / \ / \ | \ / | | X | | / \ | \___/ \___/
Left circle (1), Right circle (1), Overlapping region (1) → Total 3 distinct circular regions.
circle, overlap

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 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 17

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

Question 18

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 19

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

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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