Question

How do I find the x? What the answer

Answer 1

The height of the square pyramid is 9.8 in.

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;

`SA = a^2 + 2a \sqrt{(a^2)/(4) + h^2} \\\\96 = 4^2 + 2(4)\sqrt{(4^2)/(4)+ x^2} \\\\96 = 16 + 8√(4+ x^2) \\\\96-16 = 8√(4+ x^2)\\\\80 = 8√(4+ x^2)\\\\(80)/(8) = √(4+ x^2)\\\\10 =√(4+ x^2)\\\\ (10)^2 = 4+ x^2\\\\100 = 4 + x^2\\\\ x^2 = 100-4\\\\x^2 = 96\\\\x = √(96) \\\\x = 9.80 \ in`

Therefore, the height of the square pyramid is 9.8 in.