Question

the formulae used to calculate the area of quadrilateral is

Answer 1

The area of a quadrilateral depends on the type of quadrilateral it is.

If the figure is a regular quadrilateral there are some formulas for the areas that can be used as given below.

Square = side^2

Rectangle = L*B

Parallelogram = L*D. (D=distance between the parallel sides}

Trapezium = (a+b)*D/2

Rhombus = D1*D2/2. (D1 and D2 are the diagonals)

Kite = D1*D2/2. (D1 and D2 are the diagonals)

If the figure is an irregular quadrilateral then draw a digonal and find the areas of the two triangles so formed and add them together. There are some formulas for the areas of the triangles that can be used as given below.

Area = bh/2

Area by Heron’s formula = [s(s-a)(s-b)(s-c)}^0.5 where s =(a+b+c)/2

Area of equilateral triangle = s^2(3^0.5)/4

Area = (1/2)ab*Sin C

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Eleftherios Argyropoulos

Eleftherios Argyropoulos, B.S. Mathematics & Physics, Northeastern University (2002)

Answered Aug 25, 2018 · Author has 127 answers and 14.6k answer views

There are numerous of formulas for the evaluation of the area of a convex quadrilateral. Depending on what is given, I will propose just two of them. Assuming that we know the coordinates of the four vertices A(X1, Y1), B(X2, Y2), C(X3, Y3) and D(X4, Y4) of the quadrilateral, then the formula for its area (ABCD) will be:

(ABCD) = (1/2)[|(Χ1-X3)(Y3-Y4)-(X3-X4)(Y1-Y3)|+|(Χ1-X2)(Y2-Y3) - (X2-X3)(Y1-Y2)|]

Another evaluation formula for the area (ABCD) based on the lengths a, b, c, d of its four sides and the length r of one of its two diagonals let’s say BD is:

Let s be the semiperimeter of the triangle ABD and s’ the semiperimeter of the triangle BCD. Also let a = AB, b = AD, c = DC and d = BC. By applying Heron’s formula for both mentioned triangles, we take:

(ABCD) = sqr[s(s-a)(s-b)(s-r)] + sqr[s’(s’-d)(s’-c)(s’-r)]

Of course there are plenty of more evaluation formulas for the area (ABCD).

Answer 2

The formula to find the area of quadrilateral = 1/2 d1( h2+h2)
hope it helps u!☺☺
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