Area, Perimeter, Volume and Surface Area

Area formulas

Rectangle      = length × width
Triangle       = ½ × base × height
Parallelogram  = base × height
Trapezium      = ½ (a + b) × height
Circle         = π r²

Perimeter & circumference

• Perimeter = distance around the edge.
• Circumference = π d (or 2 π r).
• Arc length = (θ/360) × π d. Sector area = (θ/360) × π r².

Volume of prisms

Volume of prism = cross-sectional area × length
Cuboid    = length × width × height
Cylinder  = π r² × h
Pyramid   = ⅓ × base area × height
Cone      = ⅓ π r² h
Sphere    = 4/3 π r³

Surface area

Add the area of every face.

Cuboid          = 2(lw + lh + wh)
Cylinder        = 2πr² + 2πrh   (two circles + the curved side)
Sphere          = 4 π r²

Worked example

Cylinder, r = 3 cm, h = 10 cm:

Volume = π × 3² × 10 = 90π ≈ 282.7 cm³

Exam tip

Watch units: area is cm², volume is cm³. Convert all lengths to the same unit first. Leave answers "in terms of π" only if asked.