A Bretschneider Formula

★ 8/10plane geometry trigonometry Law of Cosines Triangle Geometry

Problem

A planar quadrilateral $ABCD$ has side lengths $AB = a$ , $BC = b$ , $CD = c$ , $DA = d$ , and

\cos(A + C) = \cos(B + D) = m.

Find the area $S$ of the quadrilateral in terms of $a, b, c, d, m$ .

Answer

Solution

Difficulty	8/10
Topics	plane geometry, trigonometry, Law of Cosines, Triangle Geometry

Whiteboard

Your sketch is saved only in this browser. To share it, export your drawing as an image (whiteboard menu → Export as → PNG), then upload that image in the comments below.

Discussion

Ask questions, share alternate solutions, and use LaTeX freely.

0 comments

No comments yet.