Geometry & Trig is one of the two smallest Math domains — 5–7 of the 44 questions (about 15%), the same share as Problem-Solving & Data Analysis — but it shows up reliably: triangles, circles, angles, area/volume, similarity, and right-triangle trig. Memorizing a short list of formulas makes these quick.
The reference sheet is on-screen, but looking up a formula costs time. Know the common ones cold: area, circle, Pythagorean, and SOH-CAH-TOA.
Keep these instant
- Pythagorean: a² + b² = c². Recognize the 3-4-5 and 5-12-13 triples on sight.
- Circle: area = πr², circumference = 2πr. Arc length and sector area scale with (central angle / 360).
- Triangle angles sum to 180°. Similar triangles → sides in proportion.
- SOH-CAH-TOA: sin = opp/hyp, cos = adj/hyp, tan = opp/adj.
- Radians: 180° = π radians. Multiply degrees by π/180 to convert.
Similarity shortcut: find the scale factor between one matching pair of sides, then multiply/divide every other side by it.
Worked examples
A right triangle has legs 6 and 8. Find the hypotenuse.
- Use a² + b² = c²: 6² + 8² = 36 + 64 = 100.
- c = √100 = 10.
- Shortcut: 6-8-10 is just the 3-4-5 triangle doubled. Recognizing triples saves time.
A circle has radius 6. Find the area of a 90° sector.
- Full circle area = πr² = π(6²) = 36π.
- A 90° sector is 90/360 = 1/4 of the circle.
- Sector area = (1/4)(36π) = 9π.
Two triangles are similar. The smaller has sides 3, 4, 5. The larger's shortest side is 9. Find its longest side.
- Find the scale factor using matching sides: 9 ÷ 3 = 3.
- Every side of the larger triangle is 3 times the smaller one.
- Longest side = 5 × 3 = 15.
Common mistakes to avoid
- Using the diameter when the formula calls for the radius (or vice versa). Circumference = 2πr, but also = πd — don't mix them.
- Forgetting the ½ in the triangle area formula: area = ½ × base × height.
- Matching the wrong pair of sides when finding a scale factor. Always pair shortest with shortest, longest with longest.
- Assuming a triangle is right-angled when the problem never says so. You can only use a² + b² = c² on right triangles.