The area of quadrilateral FLAX is 10 x sqrt(75).

Triangle ZAX is equilateral and has a perimeter of 30. Each side is equal and there are 3 sides (), so 30/3=10. Therefore, line XA and FL are 10 units long. Since triangle ZAX is equilateral, point Z is in the middle of line FL. Line FL is 10, so lines FZ is 5 units long. Line ZX (part of the triangle) is 10 units long. We can use the Pythagorean theorem (a^{2 }+ b^{2 }= c^{2} ) to find the length of the last line. A = 5 and C = 10. 5^{2 }= 25 and 10^{2} = 100. Therefore, 25 + b^{2} = 100. 100 - 25 = 75, so b^{2} = 75. This means that b = the square root of 75. The area would be 10*sqrt(75), or about 86.6025.

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