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Area Formulas for Geometric Figures.

Area of a geometric figure is the number of square units that can fit inside a shape. Square units can be square inches (in2),square feet (ft2), square meters (m2), etc.

Area of a triangle formulas

Triangle
  1. Area of a triangle when we know the base and the height

    The area of a triangle is equal to half of base times height.

    A = 1a · h
    2
  2. Area of a triangle when we know the lengths of all three of its sides (Heron's formula)

    A = √s(s - a)(s - b)(s - c)

  3. Area of a triangle when we know two sides and the included angle

    The area of a triangle is equal to half of a product of two sides and sine of the angle between this sides.

    A = 1a · b · sin γ
    2
    A = 1a · c · sin β
    2
    A = 1b · c · sin α
    2
  4. Area of a triangle when we know three sides and circumradius

    A = a · b · с
    4R
  5. Area of a triangle when we know semiperimeter and in-radius

    The area of a triangle is equal to semiperimeter times in-radius.
    A = s · r

    where A - the area of a triangle,
    a, b, c - the length of sides BC,AC,AB accordingly,
    h - the height, the length of the altitude,
    α, β, γ - the angles,
    r - the length of the in-radius,
    R - the length of the circumradius,
    s = a + b + c  - the semiperimeter, or half of the triangle's perimeter.
    2

Area of a square formulas

Square
  1. Area of a square when we know the length of a side

    The area of a square is equal to squared side.

    A = a2

  2. Area of a square when we know the length of diagonal

    The area of a square is half of squared diagonal.

    A = 1d2
    2

    where A - the area of a square,
    a - the lenth of side,
    d - the length of diagonal.

Area of a rectangle formula

rectangle
The area of a rectangle is equal to a product of lenghts of two sides (height and width)
A = a · b

where A - the area of a rectangle,
a, b - the length of sides(the height and width of rectangle).

Area of a parallelogram formulas

parallelogram
  1. Area of a parallelogram when we know the side and the height

    The area of a parallelogram is equal to side times height.

    A = a · h

  2. Area of a parallelogram when we know two sides and the included angle

    The area of a parallelogram is equal to a product of two sides and sine of the angle between this sides.

    A = a · b · sin α

    where A - the area of a parallelogram,
    a, b - lengths of sides,
    h - the height, the length of the altitude,
    α - the measure of the angle between sides.

Area of a rhombus formulas

rhombus
  1. Area of a rhombus when we know the side and the height

    The area of a rhombus is equal to side times height.

    A = a · h

  2. Area of a rhombus when we know length of a side and the included angle

    The area of a rhombus is equal to a product of the squared side and sine of the angle between sides of a rhombus.

    A = a2 · sin α

  3. Area of a rhombus when we know length of its diagonals

    The area of a rhombus is equal to half a product of it diagonals lengths.

    A = 1d1 · d2
    2

    where A - the area of a rhombus,
    a - the length of a side,
    h - the height, the length of the altitude,
    α - the measure of the angle between sides of a rhombus,
    d1, d2 - the length of diagonals.

Area of a trapezium formulas

trapezium
  1. Heron's formula for a trapezium

    A = a + b(s - a)(s - b)(s - a - c)(s - a - d)
    4|a - b|


  2. Area of a trapezium when we know length of 2 bases and the height

    The area of a trapezium is equal to product of the height and half-sum of two bases

    A = 1(a + b) · h
    2
    where A - the area of a trapezium,
    a, b - the length of the 2 bases,i.e., the parallel sides,
    c, d - length of the legs (the lateral sides),
    s = a + b + c + d  - the semiperimeter, or half of the trapezium's perimeter.
    2

Area of a quadrangle formulas

quadrangle
  1. Area of a quadrangle when we know length of its diagonals and angle between diagonals

    The area of a quadrangle is equal to product of its diagonals and and sine of the angle between diagonals

    A = 1d1 d2 sin α
    2

    where A - the area of a quadrangle,
    d1, d2 - the length of diagonals,
    α - the angle between diagonals.

  2. Area of a quadrangle when we know length of its perimeter and in-radius

    The area of a quadrangle is equal to perimeter timesin-radius

    A = p · r

  3. quadrangle

    Area of a quadrangle when we know length of its sides and value of opposite corners

    A = √(s - a)(s - b)(s - c)(s - d) - abcd cos2θ

    where A -the area of a quadrangle,
    a, b, c, d - the length of sides,
    s = a + b + c + d  - semiperimeter of quadrangle,
    2
    θ = α + β - half the sum of two opposite angles of a quadrilateral.
    2


Area of a rhombus circle

circle
  1. Area of a circle when we know its radius

    The area of a circle is equal to a product of squared radius and pi.

    A = π r2

  2. Area of a circle when we know its diameter

    The area of a circle is equal to a quarter product of squared diameter and pi.

    A = 1π d2
    4
    where A - the area of a circle,
    r - the length of the radius,
    d - the length of the diameter.

Area of a ellipse formulas

ellipse

The area of an ellipse is equal to a product of lengths of the major and minor semiaxes and pi.

A = π · a · b

where A - the area of an ellipse,
a - the length of the major semiaxis,
b - the length of the minor semiaxis,

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