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Formulas: the plane and space, grade 10 (3 units)

Perimeters

  • The perimeter of a rectangle – a\displaystyle a, b\displaystyle b two sides that meet at a vertex
    P\displaystyle P =\displaystyle = 2(a+b)\displaystyle 2(a+b)
  • The perimeter of a square – a\displaystyle a the side
    P\displaystyle P =\displaystyle = 4a\displaystyle 4a
  • Pi
    π≈3.14\displaystyle \pi\approx3.14
  • The circumference – d\displaystyle d the diameter
    C\displaystyle C =\displaystyle = πd\displaystyle \pi d
  • The circumference – r\displaystyle r the radius
    C\displaystyle C =\displaystyle = 2πr\displaystyle 2\pi r

Routes: Pythagoras, distance, speed and time

  • Pythagoras’ theorem – a\displaystyle a, b\displaystyle b the legs, c\displaystyle c the hypotenuse
    c2\displaystyle c^2 =\displaystyle = a2+b2\displaystyle a^2+b^2
  • The hypotenuse
    c\displaystyle c =\displaystyle = a2+b2\displaystyle \sqrt{a^2+b^2}
  • A leg
    a\displaystyle a =\displaystyle = c2−b2\displaystyle \sqrt{c^2-b^2}
  • Speed – s\displaystyle s the distance, t\displaystyle t the time
    v\displaystyle v =\displaystyle = st\displaystyle \frac{s}{t}
  • Distance
    s\displaystyle s =\displaystyle = v⋅t\displaystyle v\cdot t
  • Time
    t\displaystyle t =\displaystyle = sv\displaystyle \frac{s}{v}

Areas

  • The area of a rectangle
    A\displaystyle A =\displaystyle = a⋅b\displaystyle a\cdot b
  • The area of a square
    A\displaystyle A =\displaystyle = a2\displaystyle a^2
  • The area of a triangle – ha\displaystyle h_a the height to the side a\displaystyle a
    A\displaystyle A =\displaystyle = a⋅ha2\displaystyle \frac{a\cdot h_a}{2}
  • The area of a parallelogram – ha\displaystyle h_a the height to the side a\displaystyle a
    A\displaystyle A =\displaystyle = a⋅ha\displaystyle a\cdot h_a
  • The area of a trapezoid – a\displaystyle a, b\displaystyle b the bases, h\displaystyle h the height
    A\displaystyle A =\displaystyle = (a+b)⋅h2\displaystyle \frac{(a+b)\cdot h}{2}
  • The area of a disc – r\displaystyle r the radius
    A\displaystyle A =\displaystyle = πr2\displaystyle \pi r^2
  • A square metre in square centimetres (a dunam is 1000 m²)
    1 m2=100⋅100 cm2=10000 cm2\displaystyle 1\text{ m}^2=100\cdot100\text{ cm}^2=10000\text{ cm}^2

Tilings

  • The sum of the angles of a polygon with n\displaystyle n sides
    180∘⋅(n−2)\displaystyle 180^{\circ}\cdot(n-2)
  • The angle of a regular polygon with n\displaystyle n sides
    α\displaystyle \alpha =\displaystyle = 180∘⋅(n−2)n\displaystyle \frac{180^{\circ}\cdot(n-2)}{n}
  • The angles around a vertex of a tiling
    α1+α2+…=360∘\displaystyle \alpha_1+\alpha_2+\ldots=360^{\circ}