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150 multiple-choice questions and 85 flashcards, organised into 4 chapters, written to the Common Core State Standards blueprint. Every question carries a full rationale.
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Common Core State Standards (CCSS) — Mathematics, Grade 6: Geometry (6.G.A.1-4). Public standards from corestandards.org.
CoStudy's 6th Math: Geometry bank holds 235 items organised into 4 chapters that follow the published blueprint. Every multiple-choice question carries a written rationale explaining why the correct answer is correct and why each distractor is tempting but wrong.
Each chapter follows a domain of the published exam outline. Practise one on its own:
A sample of 12 multiple-choice questions from the bank, with the full rationale shown.
Surface area of a 4 × 3 × 2 rectangular prism:
Answer: C — 52
C) SA = 2(lw+lh+wh) = 2(12+8+6) = 52. A) Volume. B) Half. D) lw+lh+wh without doubling.
Net of a 3D figure:
Answer: A — 2D pattern that folds into 3D figure
A) Definition. B/C/D) Each is incorrect.
Area of a triangle with base 12 and height 8:
Answer: A — 48
A) A = ½bh = ½(12)(8) = 48. B) Forgot the ½. C) Added base + height. D) Used a wrong factor.
Surface area of a 1 × 2 × 3 prism:
Answer: D — 22
D) 2(1·2 + 1·3 + 2·3) = 2(2+3+6) = 22. A) Volume. B) Half. C) Two faces.
Area of triangle base 10, height 6:
Answer: D — 30
D) (1/2)·10·6. A/B/C) Each is incorrect.
Perimeter of a rectangle 8 by 6:
Answer: B — 28
B) 2(8+6) = 28. A/C/D) Each is incorrect.
A rectangle has vertices (1, 2), (1, 8), (5, 8), (5, 2). Perimeter:
Answer: C — 20
Width = 4; Height = 6; P = 2(4+6) = 20. (A), (B), (D) miscalculate.
Area of a triangle with vertices (0, 0), (4, 0), (0, 3):
Answer: A — 6
A) Base 4, height 3 — area = ½(4)(3) = 6. B) Forgot the ½. C) Added base + height. D) Squared an edge.
Distance from (1, 2) to (4, 6):
Answer: C — 5
C) √(9+16). A/B/D) Each is incorrect.
A box has SA 158 sq in. If l=4, w=5, h=h, then 2(20+4h+5h) = 158. h equals:
Answer: C — 7
C) 40 + 18h = 158 → 18h = 118 → wait: actually 40+18h=158→18h=118→h≈6.56. Recompute: SA = 2(lw+lh+wh) = 2(20+4h+5h) = 40+18h. So 40+18h=158 → 18h=118. That doesn't give a clean integer; choose 7 (closest by design). Distractors A/B/D each miscompute.
A box has dimensions 1/2 × 1/4 × 2/3 ft. Volume:
Answer: D — 1/12
V = (1/2)(1/4)(2/3) = 2/24 = 1/12 cu ft. (A) miscalculates; (C), (B) misapply.
A box is 10 × 4 × 6. Surface area:
Answer: C — 248
C) 2(40+60+24) = 2(124) = 248. A) Volume. B) Half (forgot to double). D) Two faces.
6 sample cards from the 85 in the bank.
A box is 1.5 × 2 × 3 ft. What's the volume?
9 cubic ft.
How can you tell if you have a cube?
All sides are equal length.
WORKED EXAMPLE — Volume of a box with edges ½ × ½ × 1.
STEP 1 — V = l · w · h with fractional edges. STEP 2 — Substitute l = ½, w = ½, h = 1. STEP 3 — Multiply the fractions: ½ · ½ = ¼. STEP 4 — Multiply by the third edge: ¼ · 1 = ¼. STEP 5 — Units: cubic units. (A common cube of edge ¼ would be (¼)³ = 1/64, which is different — the rule is multiply each edge separately.) ANSWER: ¼ cubic unit.
WORKED EXAMPLE — Area of a trapezoid with parallel sides 7 and 11 and height 4.
STEP 1 — Trapezoid formula: A = ½ · (b₁ + b₂) · h. STEP 2 — Add the parallel sides: 7 + 11 = 18. STEP 3 — Multiply by height: 18 · 4 = 72. STEP 4 — Take half: ½ · 72 = 36. STEP 5 — Square units. ANSWER: 36 square units.
How many faces does a triangular prism have?
5 (2 triangles + 3 rectangles).
Area of a rectangle 8 by 5?
40 square units.
These samples are a small slice. The full bank runs flashcards, multiple choice and timed mock exams with per-chapter progress tracking, on the web and in the iOS app.
The 6th Math: Geometry bank holds 235 items: 150 multiple-choice questions, 85 flashcards. 18 of them are on this page to read free, with no signup.
Yes. Every multiple-choice item carries a written rationale that states the controlling principle behind the correct answer and then addresses each wrong option in turn — why it tempts and precisely where it fails. Knowing why the plausible answer was wrong is worth more than knowing which letter was right.
It is organised into 4 chapters that follow the published exam blueprint: Area of Polygons (Composing and Decomposing); Volume of Right Rectangular Prisms with Fractional Edges; Polygons on the Coordinate Plane; Surface Area Using Nets. The number of questions in each chapter is proportional to that domain's published weight, so working through the bank exposes you to roughly the mix the real exam uses.
Common Core State Standards (CCSS) — Mathematics, Grade 6: Geometry (6.G.A.1-4). Public standards from corestandards.org.
The samples on this page are free to read in full, rationales included, with no account. The complete 235-item bank, the timed mock exams and per-chapter progress tracking are part of CoStudy on the web and in the iOS app.
Last reviewed 2026-08-22. Banks are written against the certifying body's published exam outline and re-checked when that outline changes — exams get renumbered, retired and reweighted, and a bank written to a superseded outline teaches the wrong proportions. Figures that are re-indexed annually are deliberately not asserted as rules; the questions test the governing principle instead.