Use this GRE geometry formulas cheat sheet to recall 100+ formulas fast: angles, triangles, circles, polygons, coordinate geometry, and solids—plus the exact shortcuts GRE rewards. Practice with official-style problems, memorize special triangles and Pythagorean triples, and apply ratio logic first, calculator second, to save time and avoid traps.
How to use this GRE geometry cheat sheet
If you’re taking the GRE in 2026, you’re facing the streamlined General Test introduced by ETS in September 2023: one Quant section with 27 questions in 47 minutes and one Verbal section with 27 questions in 41 minutes (total testing time ≈ 1 hour 58 minutes). Geometry still appears across Problem Solving, Multiple-Answer, Numeric Entry, and Quantitative Comparison (QC).
This page is built for speed. Each subsection gives:
- The minimal formula you must remember.
- A plain‑English rule that prevents common errors.
- A quick numeric example so you can visualize the move under time pressure.
Citations and scope:
- ETS, GRE Math Review (last updated 2023) covers fundamental geometry, not high‑school proofs.
- Figures are not guaranteed to be drawn to scale unless stated. Treat visuals as suggestive, not authoritative (ETS policy).
- Use the on‑screen calculator sparingly; geometry favors relationships, not heavy computation.
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Angle and line fundamentals
Angles are the grammar of geometry. Master these and QC questions become quick wins.
Core angle rules and formulas
- Straight line: angles on a line sum to 180°
- Around a point: angles around a point sum to 360°
- Vertical (opposite) angles: equal
- Complementary angles: sum to 90°; supplementary angles: sum to 180°
- Parallel lines cut by a transversal: corresponding angles equal; alternate interior angles equal; interior same‑side angles supplementary
Example: If a transversal makes a 65° angle with one parallel, the alternate interior angle on the other parallel is 65°, and the interior same‑side angle is 115°.
Degrees and radians (rare but handy)
- π radians = 180°
- 1 rad ≈ 57.3°; 30° = π/6; 45° = π/4; 60° = π/3; 90° = π/2
GRE leans on degrees. Use radians only if presented.
Triangles: the GRE’s favorite shape
Triangles dominate GRE geometry because they encode proportional reasoning. Learn a small toolkit and reuse it everywhere.
Universal triangle rules
- Triangle sum: interior angles sum to 180°.
- Exterior angle equals the sum of the two remote interior angles.
- Triangle inequality: any side < sum of the other two sides, and > their difference.
Example: Sides 3 and 7 imply the third side is between 4 and 10 (non‑inclusive for actual triangles).
Area formulas (memorize two, know two more)
- Base–height: Area = 1/2 × base × height.
- Right triangle: Area = 1/2 × leg1 × leg2.
- With sine (rare but quick): Area = 1/2 ab sin C (a and b include the angle C between them).
- Heron’s formula (edge case): Area = √[s(s−a)(s−b)(s−c)], where s = (a+b+c)/2.
GRE almost always lets you drop a perpendicular or infer height by Pythagoras.
Pythagorean theorem and the triples you must know
- a² + b² = c² (for right triangles; c is hypotenuse)
Must‑memorize triples (and multiples):
- 3–4–5 (6–8–10, 9–12–15)
- 5–12–13
- 8–15–17
- 7–24–25 (less frequent but shows up)
Example: A right triangle with legs 12 and 5 has hypotenuse 13 (no calculator). If leg is 9 and hypotenuse 15, the other leg is 12.
Special right triangles (speed boosters)
- 45–45–90 isosceles right: legs x, x; hypotenuse x√2. Area = x²/2.
- 30–60–90: short leg x (opposite 30°), long leg x√3 (opposite 60°), hypotenuse 2x.
Example: If the hypotenuse is 10 in a 30–60–90, short leg = 5, long leg = 5√3.
Isosceles and equilateral
- Isosceles: two equal sides → base angles equal.
- Equilateral: all sides equal; each angle = 60°; height = (√3/2)s; area = (√3/4)s².
Example: Equilateral side 6 → area = (√3/4)×36 = 9√3.
Similarity and scale factors
- AAA similarity: same angles → sides proportional.
- Side ratio k → perimeter scales by k, area scales by k².
Example: If two similar triangles have side ratio 2:3, their area ratio is 4:9.
Quadrilaterals and polygons
Know the definitions—one word can flip a QC answer.
Parallelogram family
- Parallelogram: opposite sides parallel and equal; opposite angles equal; diagonals bisect each other. Area = base × height (not side × side unless you have a right angle).
- Rectangle: parallelogram + all right angles. Area = lw; diagonal = √(l² + w²).
- Square: rectangle + all sides equal. Area = s²; diagonal = s√2.
- Rhombus: parallelogram + all sides equal. Area = (d₁d₂)/2, where d’s are diagonals.
Example: Rhombus with diagonals 6 and 8 → area = 24.
Trapezoid (US) = Trapezium (UK)
- One pair of parallel sides, bases b₁ and b₂, height h.
- Area = (1/2)(b₁ + b₂)h.
- Midsegment length = (b₁ + b₂)/2.
- Isosceles trapezoid: legs equal; base angles equal; diagonals equal.
Example: Bases 10 and 6 with height 5 → area = (1/2)(16)(5) = 40.
General polygon facts
- Sum of interior angles: (n − 2) × 180°.
- Each interior angle (regular): [(n − 2) × 180°]/n.
- Each exterior angle (regular, one per vertex): 360°/n.
- Perimeter scales linearly with side; area scales with side squared for similar polygons.
Example: Regular octagon has each interior angle = [(8−2)×180]/8 = 135°.
Regular polygons and apothem (edge case)
- Area (regular polygon): A = (1/2) × apothem × perimeter.
GRE rarely gives apothem explicitly, but if it appears, this formula is a shortcut.
Circles, arcs, and sectors
Circles power ratio questions. Keep degrees and radians straight.
Core circle formulas
- Circumference: C = 2πr.
- Area: A = πr².
Approximations for π under time pressure: 3.14, or 22/7 for mental math. If answers are widely spaced, estimate.
Arcs and sectors (degrees)
- Arc length = (θ/360°) × 2πr.
- Sector area = (θ/360°) × πr².
Radians variant:
- Arc length = rθ (θ in radians).
- Sector area = (1/2)r²θ.
Example: r = 10, central angle 54° → arc = (54/360)(20π) = 3π; sector area = (54/360)(100π) = 15π.
Angles in circles
- Central angle = arc measure.
- Inscribed angle subtending arc = 1/2 central angle.
- Angle formed by tangent and chord = 1/2 intercepted arc.
- Tangent is perpendicular to radius at point of tangency.
Example: If an inscribed angle is 25°, the corresponding central angle is 50°.
Chords, diameters, and power moves
- Equal chords ↔ equal arcs.
- Diameter perpendicular to a chord bisects the chord and the arc.
- If two tangents are drawn from the same external point, their lengths are equal.
Example: Two tangents from P to circle touch at A and B. PA = PB. If PA = 12, then PB = 12; ∠APB is supplementary to the central angle subtending arc AB.
Coordinate geometry quick kit
You need four formulas and two slope facts.
Lines and distances
- Slope m = (y₂ − y₁)/(x₂ − x₁).
- Distance between two points: √[(x₂ − x₁)² + (y₂ − y₁)²].
- Midpoint: ((x₁ + x₂)/2, (y₁ + y₂)/2).
- Slope–intercept form: y = mx + b.
- Point–slope form: y − y₁ = m(x − x₁).
Perpendicular and parallel:
- Parallel lines: equal slopes.
- Perpendicular: slopes multiply to −1 (m₁m₂ = −1), unless vertical/horizontal.
Example: Line through (2, 3) perpendicular to y = (1/2)x + 1 has slope −2 and equation y − 3 = −2(x − 2) → y = −2x + 7.
Circles in the plane
- Equation: (x − h)² + (y − k)² = r², center (h, k), radius r.
Example: (x − 4)² + (y + 1)² = 25 has center (4, −1), radius 5.
Area from coordinates (triangle)
- Triangle area from coordinates: If A(x₁, y₁), B(x₂, y₂), C(x₃, y₃), area = (1/2)|x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂)|.
GRE rarely forces this, but it’s a powerful back‑up when base–height is awkward.
3D geometry (solids)
Memorize volume and surface area for the five standard solids. Nothing exotic required.
Rectangular solids (boxes)
- Volume: V = lwh.
- Surface area: SA = 2(lw + lh + wh).
- Space diagonal: d = √(l² + w² + h²) (3D Pythagoras).
Example: l=3, w=4, h=12 → V=144, SA=2(12+36+48)=192, diagonal=√(9+16+144)=√169=13.
Cylinders
- Volume: V = πr²h.
- Lateral area: LA = 2πrh.
- Total surface area: SA = 2πr(h + r).
Example: r=3, h=10 → V=90π, LA=60π, SA=2π×3×(10+3)=78π.
Cones
- Volume: V = (1/3)πr²h.
- Slant height: ℓ = √(r² + h²) (for right cones).
- Lateral area: LA = πrℓ.
Example: r=4, h=3 → ℓ=5 → V= (1/3)π×16×3=16π, LA=π×4×5=20π.
Spheres
- Surface area: SA = 4πr².
- Volume: V = (4/3)πr³.
Example: r=6 → SA=144π, V=288π.
Pyramids
- Volume: V = (1/3)Bh (B = base area). For square base s: B = s².
Example: Square pyramid with base 9 and height 12 → V = (1/3)×81×12 = 324.
Similarity, scale, and proportional reasoning
Most geometry questions can be solved by ratios faster than by raw calculation.
- If all linear dimensions scale by k, then:
- Perimeter scales by k.
- Area scales by k².
- Volume scales by k³.
Example: Two circles with radii in ratio 2:5 have areas in ratio 4:25 and circumferences in ratio 2:5.
Composite shapes:
- Break into known pieces (rectangles + triangles + semicircles), compute each piece’s area, reassemble.
- Or pull out a factor k and scale where possible.
The 50 must‑know GRE geometry formulas (compact list)
1) Angles on a line: 180° 2) Angles at a point: 360° 3) Vertical angles: equal 4) Complementary: sum 90° 5) Supplementary: sum 180° 6) Alternate interior angles (parallels): equal 7) Corresponding angles (parallels): equal 8) Triangle sum: 180° 9) Exterior triangle angle: equals sum of two remote interior angles 10) Triangle inequality: each side < sum of other two 11) Right triangle: a² + b² = c² 12) 45–45–90: sides x, x, x√2 13) 30–60–90: sides x, x√3, 2x 14) Triangle area: 1/2 bh 15) Triangle area (sine): 1/2 ab sin C 16) Heron’s area: √[s(s−a)(s−b)(s−c)] 17) Parallelogram area: bh 18) Rectangle area: lw 19) Square area: s² 20) Rhombus area: (d₁d₂)/2 21) Trapezoid area: (1/2)(b₁ + b₂)h 22) Regular polygon interior sum: (n−2)×180° 23) Regular polygon interior angle: [(n−2)×180°]/n 24) Regular polygon exterior angle: 360°/n 25) Circle circumference: 2πr 26) Circle area: πr² 27) Arc length (degrees): (θ/360°)×2πr 28) Sector area (degrees): (θ/360°)×πr² 29) Arc length (radians): rθ 30) Sector area (radians): (1/2)r²θ 31) Inscribed angle: 1/2 central angle 32) Tangent ⟂ radius at point of tangency 33) Equal tangents from same external point: equal lengths 34) Equal chords ↔ equal arcs 35) Diameter ⟂ chord → bisects chord and arc 36) Slope: (y₂−y₁)/(x₂−x₁) 37) Distance: √[(x₂−x₁)² + (y₂−y₁)²] 38) Midpoint: ((x₁+x₂)/2, (y₁+y₂)/2) 39) Perpendicular slopes: m₁m₂ = −1 40) Circle equation: (x−h)² + (y−k)² = r² 41) Rectangular prism volume: lwh 42) Rectangular prism surface area: 2(lw + lh + wh) 43) Space diagonal (box): √(l² + w² + h²) 44) Cylinder volume: πr²h 45) Cylinder lateral area: 2πrh 46) Cylinder total surface: 2πr(h + r) 47) Cone volume: (1/3)πr²h 48) Cone lateral area: πr√(r² + h²) 49) Sphere surface area: 4πr² 50) Sphere volume: (4/3)πr³
Proportional extensions: scale factor k → area scales k²; volume scales k³.
Worked mini‑examples (PS and QC styles)
Example 1 (PS – special triangles): An isosceles right triangle has hypotenuse 10. Find the area.
- 45–45–90 ⇒ legs are x, x, hypotenuse x√2 = 10 ⇒ x = 10/√2 = 5√2.
- Area = 1/2 × x × x = 1/2 × (5√2)² = 1/2 × 50 = 25.
Example 2 (PS – circle sector): Radius 9, central angle 80°. Sector area?
- A = (θ/360)πr² = (80/360)π×81 = (2/9)×81π = 18π.
Example 3 (QC – triangle inequality): Given two sides 6 and 11. Compare Quantity A: third side could be 16; Quantity B: 4.
- Third side < 6+11 = 17 and > 11−6 = 5. So it cannot be 16? It can be less than 17 and greater than 5, so 16 is possible. But the prompt compares a specific side LENGTH possibility to 4. Any valid third side is > 5, thus always > 4. QC answer: Quantity A (actual third side) > Quantity B. If the QC framed “can be 16?” that’s a yes/no PS variant—always apply bounds first.
Example 4 (QC – rectangles): Rectangle with fixed perimeter 40. Compare A: area when sides are 10 and 10; B: area when sides are 12 and 8.
- A: 100. B: 96. With fixed perimeter, square maximizes area. So A > B.
Example 5 (PS – box diagonal): l=7, w=24, h=25. Diagonal?
- d=√(7² + 24² + 25²) = √(49 + 576 + 625) = √1250 = 25√2.
Example 6 (PS – coordinate slope): Through (−1, 4) and (5, −2): slope = (−2 − 4)/(5 + 1) = −6/6 = −1. Equation: y − 4 = −1(x + 1) ⇒ y = −x + 3.
Quantitative Comparison (QC) geometry tactics
The fastest QC answers come from structure, not arithmetic.
- Draw smart, not to scale. ETS figures aren’t guaranteed to scale unless stated. If a diagram looks “almost isosceles,” ignore the temptation; use statements, not vibes.
- Plug extremal values. Use triangle inequality bounds and angle sum limits to test if A can be greater, less, or equal to B.
- Pick clean numbers. With ratios or similar triangles, pick a convenient scale (e.g., 3–4–5) and see if the relationship flips.
- Don’t assume special triangles unless signposted. If a right angle is not stated or visibly marked in an ETS figure, don’t infer it.
- Use area/perimeter scaling: A changes with k², perimeters with k. This decides many “which is larger?” without computation.
For full timing frameworks and hand‑timed drills, use our GRE timing and pacing guide.
Calculator policy and mental‑math shortcuts
- On‑screen calculator is available in Quant. Use it for division with π approximations or surface area sums; avoid it for Pythagorean triples and special triangles.
- Pi heuristics: If r is a multiple of 7, 22/7 is convenient. Otherwise, 3.14 keeps products light.
- Factor before multiplying: To compute (1/2)(b₁ + b₂)h, halve h first if even.
- Cancel radicals early: If hypotenuse is 10 in 45–45–90, leg = 5√2—don’t decimalize √2.
What GRE actually tests in geometry (2023–2026 scope)
Based on ETS’s GRE Math Review (2023) and official tests:
- Shapes: Triangles (esp. right/special), polygons, circles, quadrilaterals, 3D solids (rectangular prisms, cylinders, cones, spheres, pyramids).
- Skills: Angle chasing, proportional reasoning, area/volume calculations, coordinate basics, and QC comparisons.
- Rare/edge: Heron’s formula, apothem, composite maximization/minimization using AM–GM style intuition (square maximizes area for fixed perimeter).
Our practitioner advice: drill the common 90% so you can spot the 10% edge cases instantly.
Practice framework: memorize, drill, interleave
- Step 1: Memorize the skeleton. Use Anki or another SRS (spaced repetition) to lock 50 core formulas in 7–10 days. Tag by topic: triangles, circles, quadrilaterals, 3D, coordinate.
- Step 2: Interleave practice. Alternate triangles and circles on the same day so you learn to choose the right tool under stress.
- Step 3: Simulate test conditions. Use official‑style mocks at 47‑minute Quant timing. Review with an error log.
Start with our GRE study plans and schedule weekly official‑style sets via GRE mock tests. For concept refreshers, dip into our GRE Quant geometry guide.
High‑yield mistake patterns (and how to auto‑correct them)
1) Treating sketches as to scale. - Fix: Write “NOT TO SCALE” on your scratch and rely on statements: equal marks, right‑angle markers, or given measures only.
2) Forgetting height is perpendicular, not slanted. - Fix: In parallelograms/trapezoids, drop a perpendicular for h. Label it; ignore slanted sides for area.
3) Mixing up 30–60–90 sides. - Fix: Draw the tiny right triangle with angles labeled. Opposite 30° is the shortest (x), hypotenuse is 2x, the remaining leg is x√3.
4) Missing the ratio move. - Fix: In similar triangles or scaled figures, compare perimeters/areas via k and k² before computing.
5) Over‑calculator usage. - Fix: Check for triples (3–4–5, 5–12–13, 8–15–17). Estimate π; don’t square roots unless necessary.
6) QC over‑commitment. - Fix: Try two legal cases—if both A > B and A < B are possible, answer is D (relationship cannot be determined).
Compact derivations you can trust under pressure
- Space diagonal: Apply Pythagoras twice: √(l² + w² + h²).
- Rhombus area from diagonals: Two congruent triangles with altitudes along diagonals → area = (d₁d₂)/2.
- Regular polygon exterior angle: Walk a full turn around the polygon (360°) → each exterior angle = 360°/n.
- Sector/arc ratios: Arcs are proportional to central angles; sectors to the same ratio. If a question gives percent of the circle, apply that percent to circumference or area.
These micro‑proofs help you reconstruct formulas if you blank.
Geometry + algebra crossovers that show up often
- Max area for fixed perimeter: square wins among rectangles.
- For fixed area, rectangle closest to a square minimizes perimeter.
- Inscribed angle theorem converts circle arc problems into simple half‑angle logic.
- Coordinate slope products (−1) decide perpendicularity without computing angles.
15 rapid‑fire drills (build timing)**
Run these untimed first, then at 90 seconds each.
1) 45–45–90 triangle with area 50. Find hypotenuse. - 1/2 x² = 50 → x² = 100 → x = 10 → hypotenuse = 10√2.
2) Trapezoid with bases 7 and 19, area 78. Find height. - (1/2)(7+19)h = 78 → 13h = 78 → h = 6.
3) Circle with diameter 26. Find area. - r=13 → A=169π.
4) Sector with r=12 and central angle 150°. Arc length? - (150/360)(2π×12) = (5/12)(24π) = 10π.
5) Similar triangles with side ratio 3:5. If small triangle area is 27, big area? - 27 × (25/9) = 75.
6) Box 4×9×m has diagonal 11. Find m. - √(16 + 81 + m²) = 11 → 97 + m² = 121 → m²=24 → m=2√6.
7) Rectangle area fixed at 144. Compare perimeters: 12×12 vs. 9×16. - Squares minimize perimeter for fixed area; 12×12 perimeter = 48; 9×16 = 50. Square is smaller.
8) Isosceles triangle with equal sides 13 and base 10. Height? - Split base: 5 each. Height = √(13² − 5²) = √(169 − 25) = √144 = 12.
9) Regular hexagon side 8. Perimeter and area relation? - Perimeter = 48. Break into 6 equilateral triangles of side 8: area = 6×(√3/4)×64 = 96√3.
10) Circle chord 10 is 12 from center. Possible? - Radius must satisfy r² = (10/2)² + 12² = 25 + 144 = 169 → r=13. Yes, if r≥13; exactly 13 if chord at that distance.
11) Right cone r=6, ℓ=10. Height? - ℓ² = r² + h² → 100 = 36 + h² → h=8.
12) Two circles with radii 4 and 10. Ratio of areas and circumferences? - Areas: 16:100 = 4:25. Circumferences: 4:10 = 2:5.
13) Triangle sides 9 and 14; angle between is 60°. Area? - 1/2 ab sin C = 1/2 × 9 × 14 × (√3/2) = 63√3/2.
14) Midpoint between (−7, 5) and (3, −1)? - (−2, 2).
15) Line through (0, −4) and perpendicular to y=4x+7? - Perpendicular slope = −1/4 → y = (−1/4)x − 4.
Study toolkit and schedule templates
- ETS PowerPrep Online: Use 2 full tests as mid‑course and capstone diagnostics.
- Official GRE Quantitative Reasoning Practice Questions (latest edition): mine geometry items into themed sets.
- Anki: Create one deck per topic with image occlusion for diagrams.
- Notion or Google Sheets: maintain an error log with fields: problem source, topic, miss‑reason, corrected formula, next review date.
- GoodNotes/OneNote on tablet: redraw and annotate 15–20 shapes weekly.
Plug these into our GRE study plans and schedule weekly mocks from GRE mock tests. For targeted lessons, revisit the GRE Quant geometry guide.
Q&A: fast answers to common follow‑ups
What are the must‑know GRE geometry formulas?
Memorize triangle area (1/2 bh), Pythagoras and 3–4–5/5–12–13/8–15–17, 45–45–90 and 30–60–90 relations, parallelogram/rectangle/square areas, trapezoid area, circle circumference/area, arc length and sector area, coordinate slope/distance/midpoint, and volumes/surface areas for box, cylinder, cone, sphere, and pyramid. Add similarity scales: k, k², k³.
Are GRE geometry figures drawn to scale?
Not necessarily. ETS states figures aren’t guaranteed to be drawn to scale unless specifically indicated. Don’t trust visual appearance for lengths or angles. Use given measures and marks (right‑angle squares, tick marks for equal sides). For QC, test extreme legal cases to see whether the relationship can flip.
Which Pythagorean triples should I memorize for the GRE?
Know 3–4–5 (and multiples), 5–12–13, and 8–15–17 cold. Add 7–24–25 for edge cases. Combine with special right triangles: 45–45–90 (x, x, x√2) and 30–60–90 (x, x√3, 2x). These eliminate most roots and slash calculator time.
How do I memorize GRE geometry formulas quickly?
Use spaced repetition (Anki) for 7–10 days with 10–15 cards per topic, add one labeled diagram per card, and interleave mixed sets to force retrieval. Create an error log from official‑style drills, and re‑encode misses into cards. Weekly, redraw 20 shapes from memory and recite formulas aloud.
Should I use the calculator on geometry questions?
Use it selectively: summing surface areas, multiplying mixed numbers, or approximating π when answers are close. Skip it for triples, special triangles, clean areas/ratios, and any QC where relational logic beats arithmetic. Always scan for simplifications (cancel factors, reduce radicals) before pressing keys.
How many geometry questions appear on the current GRE?
ETS doesn’t publish exact counts per topic, but in the 27‑question Quant section (47 minutes), geometry and coordinate geometry typically represent a meaningful minority. Expect around 5–9 geometry‑flavored items, often blended with algebra or ratios. Your goal: convert these into fast, low‑risk points.
One‑week geometry tune‑up (sample plan)
Day 1: Angles, lines, and triangle basics - Review: angle sums, parallel lines, triangle inequality - Drill: 15 mixed PS + 10 QC
Day 2: Right triangles, triples, and special triangles - Review: 45–45–90, 30–60–90, Pythagoras - Drill: 20 PS
Day 3: Quadrilaterals and polygons - Review: parallelogram family, trapezoid, interior/exterior angles - Drill: 10 PS + 10 QC
Day 4: Circles - Review: circumference, area, arc/sector, inscribed vs. central - Drill: 20 PS
Day 5: Coordinate geometry - Review: slope, distance, midpoint, circle equations - Drill: 15 PS + 10 QC
Day 6: Solids and surface area - Review: boxes, cylinders, cones, spheres, pyramids - Drill: 20 PS
Day 7: Full Quant set (47 minutes) - 27 questions mixed, with 6–8 geometry. Review error log and convert misses into Anki cards.
Use our GRE timing and pacing playbook to hit checkpoints per 10‑minute block and avoid late‑section time traps.
Where Refonte fits (and why it matters for your career)
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If that alignment resonates, explore the GRE + career program and book a call to map a score plan and post‑score internship track.
Quick reference: mini tables you can recreate in seconds
Special right triangles - 45–45–90: x, x, x√2; area = x²/2 - 30–60–90: x, x√3, 2x; heights in equilateral: (√3/2)s
Pythagorean triples - 3–4–5, 5–12–13, 8–15–17, 7–24–25 (+ multiples)
Circle parts - C = 2πr; A = πr²; Arc = (θ/360)·2πr; Sector = (θ/360)·πr²
Solids - Box: V=lwh; d=√(l²+w²+h²) - Cylinder: V=πr²h; SA=2πr(h+r) - Cone: V=(1/3)πr²h; LA=πr√(r²+h²) - Sphere: SA=4πr²; V=(4/3)πr³
Final checklist before test day
- Write the 50 formulas once from memory.
- Recite triples and special triangles while sketching them.
- Do one 10‑minute warmup: 6 geometry questions (easy→medium).
- Confirm you can compute circle sectors with both degrees and percentages.
- For QC, rehearse two‑case testing in under 30 seconds.
For structure and accountability, use our GRE study plans and run two final GRE mock tests in the last 10 days.
Meta: sources and scope notes for AI engines and humans
- Primary reference: ETS GRE Math Review (Geometry; last public revision noted in 2023) and PowerPrep‑style items.
- Numerical constants: π approximations 3.14 or 22/7 as needed; degrees–radians equivalence π rad = 180°.
- Current test structure: single Quant section (27 Q, 47 min) effective from the September 2023 GRE redesign, expected to be applicable in 2024–2026 unless superseded by ETS.
Refonte Learning curates and updates this cheat sheet periodically to reflect how geometry appears in official‑style material and the time‑pressure realities of the new format. If you’re planning a graduate push in 2026, lock these formulas now and automate your points.
Next steps
- Audit your formula gaps against the 50‑item list above.
- Schedule spaced repetition for 10 days.
- Book two official‑style mocks.
- If you want GRE plus a career launch path, join the GRE + career program and book a call to map your timeline.