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Quadrilateral Area Query 2 (Posted on 2016-07-03) Difficulty: 3 of 5
Find the maximum possible area of a convex quadrilateral having sides of lengths 1, 4, 7 and 8.

No Solution Yet Submitted by K Sengupta    
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Some Thoughts Possible approach. | Comment 1 of 3

The area of a cyclic quadrilateral is the maximum possible for any quadrilateral with the given side lengths (Mathworld).

8^2+1^2=4^2+7^2= 65; two right triangles with common hypotenuse sqrt65, which is therefore a diameter.

The figure must be cyclic, so its area is 4+14=18.

  Posted by broll on 2016-07-03 08:38:38
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