Ideas in Geometry/Instructive examples/Section 3.2 Problem 7-Using Brahmagupta's Formula

Find the area of the quadrilateral that can be inscribed in a circle whose sides are of lengths 2, 5, 6, and 3. Explain your work.

Using Brahmagupta's Formula, the area of a quadrilateral that can be inscribed in a circle is the square root of (p/2-a)(p/2-b)(p/2-c)(p/2-d) where p is the perimeter of the quadrilateral and a,b,c, and d are the side lengths of the quadrilateral.

The perimeter of the quadrilateral is 2+5+6+3=16.

Therefore: area=square root of (16/2-2)(16/2-5)(16/2-6)(16/2-3)= square root of (6)(3)(2)(5)= square root of 180= 6 square root(5)