Mathematics · Grades 9–10
Geometry · Formula sheet
Rules, conditions and small examples in one printable reference.
Remember this
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
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
Further reading and review references
These are reference links, not copied exercises, institutional endorsement or proof of independent review.
Learning preview · teacher review required. Grade bands are approximate, not official curriculum alignment.