Formulas and rules

Perimeter and area

perimeter = sum of sides; rectangle area = l x w

Perimeter is the distance around a shape, area is the surface inside it.

Area of a triangle

area = (base x height) / 2

Half the base times the perpendicular height.

Circle area and circumference

area = pi r^2 ; circumference = 2 pi r

Pi is roughly 3.14. The diameter is twice the radius.

Angle rules

triangle = 180 deg; straight line = 180 deg; full turn = 360 deg

Angles in a triangle add to 180. On a straight line they add to 180. Angles at a point add to 360.

Pythagoras theorem

a^2 + b^2 = c^2

In a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides.

Thales theorem

AM/AB = AN/AC = MN/BC

A line parallel to one side of a triangle cuts the other two sides proportionally.

Volume

box = l x w x h; cylinder = pi r^2 h

Volume measures the space inside a solid, in cubic units.

Symmetry

A shape has a line of symmetry when it folds exactly onto itself.

Coordinates

A point (x, y) gives the horizontal then vertical position. x comes before y.

Vectors

u + v = (x1 + x2, y1 + y2) ; |u| = sqrt(x^2 + y^2)

Add vectors component by component. The length is found with Pythagoras.