4. Surface area of a square pyramid is 160cm^2. The area of the lateral triangles is 96cm^2. What is length of one of the sides.
To solve this problem, we first need to understand the formula for the surface area of a square pyramid. The surface area of a square pyramid is given by the formula:
Surface Area = Base Area + (0.5 * Perimeter * Slant Height)
Since the base of the square pyramid is a square, the base area can be calculated by: side^2.
Given that the surface area of the square pyramid is 160cm^2 and the lateral area of the triangles is 96cm^2, we can set up the following equations:
160 = side^2 + 96
Subtracting 96 from both sides gives:
side^2 = 64
Taking the square root of both sides gives:
side = 8cm
Therefore, the length of one of the sides of the square pyramid is 8cm.