Answer:
(264+24√21) in²
Step-by-step explanation:
Area of a square = Length * Length
A = L²
Given the length of a square as [tex]2\sqrt{3}+6\sqrt{7}[/tex] inches' The area of the square will be calculated as shown;
[tex]A = (2\sqrt{3}+6\sqrt{7})^2\\\\A = (2\sqrt{3}+6\sqrt{7})(2\sqrt{3}+6\sqrt{7})\\\\A =(2\sqrt{3})(2\sqrt{3})+(2\sqrt{3})(6\sqrt{7})+(6\sqrt{7})(2\sqrt{3})+(6\sqrt{7})(6\sqrt{7})\\\\A = 4\sqrt{9}+12\sqrt{21}+12\sqrt{21}+36\sqrt{49}\\\\A = 4(3)+24\sqrt{21}+36(7)\\ \\A = 12+24\sqrt{21}+252\\\\A = 264+24\sqrt{21}[/tex]
Hence the area of the square is (264+24√21) in²
