#2**+1 **

30-60-90 triangles override this problem. If AE=24, then AB=\(\frac{24}{2}\sqrt{3}=12\sqrt{3}.\) BE is equal to twelve inches, and this is opposite to the ninety(90) degrees angle in triangle BCE. And, CE=6 inches, while BC is equal to \(6\sqrt{3}\) inches. Thus, opposite to the ninety-degrees in the triangle CDE, means that ED=three inches, and CD equals \(3\sqrt{3}\) inches. Thus, the perimeter of quadrilateral ABCD is \(12\sqrt{3}+6\sqrt{3}+3\sqrt{3}+24+3=21\sqrt{3}+27\) inches.

.tertre Jun 22, 2019