Polygons, Geometry For GMAT Notes | Study Quantitative Aptitude for GMAT - GMAT

GEOMETRY 

Polygons

Polygons include any shape with 4 or more sides and usually involve calculating an area or perimeter.

Circles

ALL circle questions come down to the RADIUS. With the radius, you can solve almost any question. When a circle interacts with another shape, pay careful attention to how the radius factors into that other shape.

Area = πr²
circumference = 2πr
Sector Area: A fraction of the area
Arc Length: A fraction of the circumference

Example:
Area = 36π
Sector Shaded (90° is a quarter of the circle) = 9π
Circumference =  12π
Arc (90° carves a quarter of the circumference) = 3π

Multi-Shape

These shapes will always vary. Nevertheless, they are always combinations of the other GMAT geometry rules, and therefore rarely contains any unique rules. Break this shapes apart by looking for shapes you’re familiar with.

Note: Multi-Shape generally show up 1 time on Test Day, can take 3 minutes to solve, and tend to be worth very little (and sometimes nothing). Your best move on these questions is typically to TRIAGE.

Solids

Solid questions involve rectangular solids (boxes), cubes (a type of rectangular solid in which all dimensions are the same) and cylinders (cans or tubes). They usually involve volume (what the solid will “hold”) and sometimes surface area.

Volume = base x width x height
Surface Area (Sum of the faces) =  Sum of: 2(base x width) 2(width x height) 2(base x height)

Volume = πr²h  
Surface Area (top + bottom + side) =  2πr² + 2πr