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What is the formula for finding the area of a Quadrilateral?

Ok so I need to know this. You know how the area of a triangle is 1/2basexheight I need to find some formula like that.

The formula for the area of an arbitrary quadrilateral is

√[(a+b+c-d)(a+b-c+d)(a-b+c+d)(-a+b+c+d) - 16 abcd cos(q)^2]

where q is half the sum of two opposite angles. For a cyclic
quadrilateral the each pair of opposite angles sums to pi, so it
reduces to Brahmagupta’s formula as under.

√[(a+b+c-d)(a+b-c+d)(a-b+c+d)(-a+b+c+d)].

[Brahmgupta was the Indian mathematician born in 598 A.D. who gave the formula for area of a cyclic quadrilateral.]

Edit:
a, b, c and d are the lengths of the sides of the quadrilateral.

This entry was posted on Saturday, June 19th, 2010 at 6:38 am and is filed under area formula. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.

5 Responses to “What is the formula for finding the area of a Quadrilateral?”

  1. A quadrilateral can be divided into two triangles.
    References :

  2. mathsmanretired on June 19th, 2010 at 12:49 pm

    There is no formula for finding the area of a quadrilateral unless you know more about it. This is because quadrilaterals with the same side lengths can have very different areas depending on their corner angles.
    References :

  3. depends on the shape
    for rectangle = L × B
    square = L²
    parallelogram = base × height
    for rhombus or kite 1/2 × product of diagonals
    for trapezium = 1/2 h(a + b) ——— where h is height and a and b are parallel sides.
    ——
    References :

  4. A square is a quadrilateral. All sides are the same length. S (side) squared is the area.
    For a rectangle, the area is defined by length times width.
    For other quadrilaterals, the formulas are somewhat similar, but for an irregular quadrilateral (the shape of an arrow point or something else that is an odd shape) can be divided into triangles in order to find the area.
    References :

  5. Madhukar Daftary on June 19th, 2010 at 2:04 pm

    The formula for the area of an arbitrary quadrilateral is

    √[(a+b+c-d)(a+b-c+d)(a-b+c+d)(-a+b+c+d) - 16 abcd cos(q)^2]

    where q is half the sum of two opposite angles. For a cyclic
    quadrilateral the each pair of opposite angles sums to pi, so it
    reduces to Brahmagupta’s formula as under.

    √[(a+b+c-d)(a+b-c+d)(a-b+c+d)(-a+b+c+d)].

    [Brahmgupta was the Indian mathematician born in 598 A.D. who gave the formula for area of a cyclic quadrilateral.]

    Edit:
    a, b, c and d are the lengths of the sides of the quadrilateral.
    References :
    http://www.mathpages.com/home/kmath196.htm

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