Mathematics · Grades 6–8

Geometry · Formula sheet

Rules, conditions and small examples in one printable reference.

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Pythagorean theorem

The hypotenuse is opposite the right angle and is the longest side.

a² + b² = c² (right triangle)

√(232² + 435²) = √243049 = 493

Area of a circle

Use the radius, not the diameter. These exercises request the coefficient of π.

A = πr²

A = π × 27² = 729π → k = 729

Circumference of a circle

The diameter is twice the radius.

C = 2πr = πd

C = 2 × π × 25 = 50π

Area of a trapezoid

a and b are the parallel sides; h is the perpendicular distance between them.

A = (a + b)h/2

(13 + 21) × 22 ÷ 2 = 374

Volume of a cylinder

Multiply circular base area by perpendicular height.

V = πr²h

V = π × 15² × 19 = 4275π

Interior angles of polygons

For a simple polygon, n is the number of sides and n ≥ 3.

sum = (n − 2) × 180°

(29 − 2) × 180 = 4860

Find a missing rectangle side

Use consistent length and area units.

width = area ÷ length

648 ÷ 27 = 24

Volume of two joined boxes

Add the volumes only when the boxes do not overlap.

V = l₁w₁h₁ + l₂w₂h₂

336 + 24 = 360

Volume of a cone

Use the perpendicular height and radius, not the diameter.

V = πr²h/3

3.14 × 2² × 90 ÷ 3 = 376.8

Scale factors and area

A length scale factor k changes area by k squared.

new area = old area × k²

64 × 2² = 256