Geometry 3D Shape Formulas

Area of a Rhombus or Kite

Area=1/2 d,d2

Parts of a regular polygon

center, radius, central angle (angle between two radii), apothem (distance from center to a side).

Area of a regular polygon

A=1/2 aP

Perimeter of a regular polygon

P=sn

Circumference

C=2pir OR C=pid

Arc length of a circle

arc length of AB/2PIr=mAB/360

Area of a circle

A=PIr²

Population Density

PD=# of people/area of land

Area of a sector

Area of sector/PIr²=mAB/360

Euler’s Formula

vertices+faces=edges+2

Polyhedra

A solid bounded by polygons. EX: Prism, Pyramid

Not polyhedra

Cylinder, cone, sphere

Cavalieri’s Principle

If two solids have the same height and the same cross-sectional area at every level, then they have the same volume.

Volume of a Prism

V=Bh

Volume of a cylinder

V=Bh=PIr²h

Volume of a pyramid

V=1/3Bh

Density Formula

density=mass/volume

Similar solids

r1/r2=a/b V1/V2=a³/b³

Surface area of a prism

S=2B+Ph

Surface area of a cylinder

S=2B+Ch=2PIr²+2PIrh

Surface area of a pyramid

S=B+1/2PL

Surface area of a cone

S=PIr²=PIrL

Volume of a cone

V=1/3Pir²h

Surface area of a sphere

S=4PIr²

Volume of a Sphere

V=4/3PIr³