The formula for the area of a cyclic quadrilateral is:
√(s−a) (s−b) (s−c) (s−d)
Where “s” is called the semi-perimeter,
s = a + b +c + d / 2
Example 1
Calculate the area of the quadrilateral when the sides of the quadrilateral are 30 m, 60 m, 70 m and 45 m.
Solution
Given parameters are
a=30m
b = 60m
c = 70m
d = 45m
s = a + b +c + d / 2
s = 30+60+70+45 / 2
s = 102.5 m
Area of cyclic quadrilateral is given by
= √ (s−a) (s−b) (s−c) (s−d)
= √(102.5−30)(102.5−60)(102.5−70)(102.5−45)
= 2399.60 square meter
Example 2
Calculate the area of the quadrilateral when the sides of the quadrilateral are 35 m, 77 m, 75 m and 43 m.
Solution
Given parameters are
a = 35 m
b = 77 m
c = 75 m
d = 43 m
s = a + b + c + d / 2
s = 35 + 77 + 75 + 43 / 2
s = 115 m
Area of cyclic quadrilateral is given by
√(s−a) (s−b) (s−c) (s−d)
= √ (115−35)(115−77)(115−75)(115−43)
2958.91 square meter