This is Not a Square
A quadrilateral having sides of length 3, 4, 5 and 6 units is inscribed in a circle.
The area of this quadrilateral can be expressed as , where and are coprime positive integers. Find .
The answer is 8.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
Relevant wiki: Brahmagupta's Formula
Area of a cyclic quadrilateral with lengths of four sides given is
A r e a = ( s − a ) ( s − b ) ( s − c ) ( s − d )
s = 2 a + b + c + d = 2 3 + 4 + 5 + 6 = 9
s − a = 9 − 3 = 6
s − b = 9 − 4 = 5
s − c = 9 − 5 = 4
s − d = 9 − 6 = 3
A r e a = ( 6 ) ( 5 ) ( 4 ) ( 3 ) = 2 ( 3 ) 2 ( 5 )
A + B = 3 + 5 = 8