Mastering SAT Spatial Reasoning: Geometry & Trigonometry

Area of a Rectangle

A = lw

Area of a Triangle

A = \frac{1}{2}bh

Area of a Parallelogram

A = bh

Volume of a Rectangular Prism

V = lwh

Surface Area of a Rectangular Prism

Surface Area = 2(lw + lh + wh)

Volume of a Cylinder

V = \pi r^2 h

Surface Area of a Cylinder

Surface Area = 2\pi r^2 + 2\pi r h

Volume of a Sphere

V = \frac{4}{3}\pi r^3

Volume of a Cone

V = \frac{1}{3}\pi r^2 h

Linear Scale Factor

Ratio of lengths between similar shapes is k.

Area Ratio

For similar shapes, area ratio is k^2.

Volume Ratio

For similar shapes, volume ratio is k^3.

Triangle Sum Theorem

The sum of interior angles of a triangle is always 180 degrees.

Exterior Angle Theorem

An exterior angle is equal to the sum of the two opposite interior angles.

Isosceles Triangle Theorem

If two sides are equal, the opposite angles are equal.

Congruent Triangles

Triangles that are identical in shape and size.

Similar Triangles

Triangles that have the same shape but different sizes.

Pythagorean Theorem

In a right triangle, a^2 + b^2 = c^2.

45-45-90 Triangle Ratios

Sides are x, x, x\sqrt{2}.

30-60-90 Triangle Ratios

Sides are x (opposite 30), x\sqrt{3} (opposite 60), 2x (hypotenuse).

Sine Definition

\sin(\theta) = \frac{\text{Opposite}}{\text{Hypotenuse}}.

Cosine Definition

\cos(\theta) = \frac{\text{Adjacent}}{\text{Hypotenuse}}.

Tangent Definition

\tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}}.

Equation of a Circle

(x - h)^2 + (y - k)^2 = r^2.

Arc Length in Radians

s = r\theta.

Sector Area in Radians

A = \frac{1}{2} r^2 \theta.