Answer:
The height of the square pyramid is 9.8 in.
Step-by-step explanation:
Given;
area of the square pyramid, A = 96 in²
base length, a = 4 in
height of the pyramid, h = x in
The surface area of the pyramid is calculated as follows;
[tex]SA = a^2 + 2a \sqrt{\frac{a^2}{4} + h^2} \\\\96 = 4^2 + 2(4)\sqrt{\frac{4^2}{4}+ x^2} \\\\96 = 16 + 8\sqrt{4+ x^2} \\\\96-16 = 8\sqrt{4+ x^2}\\\\80 = 8\sqrt{4+ x^2}\\\\\frac{80}{8} = \sqrt{4+ x^2}\\\\10 =\sqrt{4+ x^2}\\\\ (10)^2 = 4+ x^2\\\\100 = 4 + x^2\\\\ x^2 = 100-4\\\\x^2 = 96\\\\x = \sqrt{96} \\\\x = 9.80 \ in[/tex]
Therefore, the height of the square pyramid is 9.8 in.
