# SAT geometry: what’s on the reference sheet, and what to memorize

> SAT geometry is a small, predictable slice of Math, and the test hands you most formulas. Here’s what’s given, what to memorize, and the shapes that recur.

Published 2026-06-26 | Math | StudyHall

Canonical: https://trystudyhall.com/blog/sat-geometry-formulas

Geometry is one of the smaller, more predictable parts of the Digital SAT: a handful of Math questions, and the test prints most of the formulas right at the start of the section. The win isn’t memorizing everything. It’s knowing what you’re given for free, the short list you actually have to know cold, and the four shapes that keep showing up.

**Key takeaways:**
- **It’s all in Math, and it’s not much:** expect roughly a handful of geometry and trig questions across the two Math modules.
- **The reference sheet is given:** circle area and circumference, triangle and rectangle area, the Pythagorean theorem, the special right triangles, and the volume formulas are all printed for you.
- **Memorize what isn’t printed:** angle relationships, the triangle angle sum of $180°$, and SOH-CAH-TOA.
- **Radius vs. diameter** is the single biggest source of careless errors. Read which one the problem gives before you compute.

## What the SAT hands you for free

Every Math module opens with a reference sheet. You never have to recall these, so don’t waste memory on them. Instead, learn to recognize which one a question is reaching for.

| Given on the reference sheet | You memorize |
| --- | --- |
| Circle: area πr², circumference 2πr | Vertical angles are equal |
| Pythagorean theorem: a² + b² = c² | Angles on a line sum to 180° |
| Special right triangles: 30-60-90, 45-45-90 | Triangle angles sum to 180° |
| Volume: box, cylinder, sphere, cone | SOH-CAH-TOA (right-triangle trig) |
| Area of a triangle: ½ b h | Arc and sector are fractions of the whole |
*Don’t memorize the left column. Do memorize the right.*

## The four shapes that show up

Almost every geometry question is one of four things: an angle chase, a right triangle, a [circle](https://trystudyhall.com/blog/sat-circles), or [area/volume](https://trystudyhall.com/blog/sat-area-and-volume). Name which one you’re looking at first; the right move follows from that.

1. **Angles.** Use the relationships: vertical angles are equal, a straight line is $180°$, and parallel lines cut by a transversal make equal corresponding and alternate angles. Name the relationship, then the algebra is just bookkeeping. The [angles and triangles guide](https://trystudyhall.com/blog/sat-angles-and-triangles) drills that angle-chasing method on its own.
2. **Right triangles.** Spot the right angle, label the hypotenuse (always opposite it), then reach for the Pythagorean theorem or, if the angles are $30/60/90$ or $45/45/90$, the special-triangle ratios from the sheet.
3. **Circles.** Pin down what you’re given (radius, diameter, area, or circumference) and what’s asked. An arc length or sector area is just that fraction of the whole, set by the central angle over $360°$.
4. **Area and volume.** Match the shape to its formula and check the units. The trap is plugging a diameter in where the formula wants a radius.

## See it once

A right triangle with legs $3$ and $4$ has hypotenuse $5$, because $3^2 + 4^2 = 9 + 16 = 25 = 5^2$. The $3$-$4$-$5$ triangle (and its multiples like $6$-$8$-$10$) shows up constantly, so it’s worth recognizing on sight:

*Figure: The 3-4-5 right triangle: legs 3 and 4, hypotenuse 5. The square marks the right angle.*

> **Watch out: Radius, diameter, and "not drawn to scale"** Half of all circle mistakes are using a diameter where the formula wants a radius (the radius is half the diameter). And when a figure says "not drawn to scale," never measure or eyeball it. Use only the relationships the problem states.

## Try one

**Example: Circles.**

A circle has a diameter of $10$. What is its area?

- A) $10\pi$
- B) $25\pi$
- C) $100\pi$
- D) $20\pi$

**Answer:** B. The diameter is 10, so the radius is half of that: r = 5. Area is πr² = π(5)² = 25π. The trap answer 100π comes from using the diameter (10) as the radius. Always halve the diameter first.

> **Tip: Trig, when it appears** Right-triangle trig is rare but easy points: SOH-CAH-TOA ($\sin = \frac{\text{opp}}{\text{hyp}}$, $\cos = \frac{\text{adj}}{\text{hyp}}$, $\tan = \frac{\text{opp}}{\text{adj}}$). One identity worth knowing: $\sin(x) = \cos(90° - x)$. The [right triangles and trigonometry course](https://trystudyhall.com/learn/right-triangles-and-trigonometry) covers the rest.

**[Drill SAT geometry](https://trystudyhall.com/bank/lines-angles-and-triangles)**: Work angles, triangles, and circles with a tutor that asks for the relationship before the arithmetic.

## FAQ

### Are geometry formulas given on the SAT?

Most are. Each Digital SAT Math module opens with a reference sheet that includes circle area and circumference, the Pythagorean theorem, the special right triangles, triangle and rectangle area, and the volume formulas. You memorize the things not printed there: angle relationships, the 180-degree triangle angle sum, and SOH-CAH-TOA.

### How much geometry is on the Digital SAT?

Not much. Geometry and Trigonometry is the smallest of the four Math content areas, usually a handful of questions across the two Math modules. It’s worth a focused review precisely because it’s small and predictable.

### What’s the fastest way to handle circle questions?

Decide what you’re given (radius, diameter, area, or circumference) and what’s asked, and keep radius vs. diameter straight, since the radius is half the diameter. Arc length and sector area are just the central-angle fraction (angle over 360) of the full circumference or area.

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