Final answer:
To find the length of a side of the base and the slant height of a square pyramid, we can use the formulas for lateral area and surface area of a square pyramid.
Step-by-step explanation:
To find the length of a side of the base and the slant height of a square pyramid, we can use the formulas for lateral area and surface area of a square pyramid.
Let's denote the length of a side of the base as 's' and the slant height as 'l'.
The formula for the lateral area of a square pyramid is given by: Lateral Area = (Perimeter of Base) * (Slant Height) / 2. Since a square has all sides equal, the perimeter of the base is 4s. Therefore, we can rewrite the formula as: 118 = 4s * l / 2.
The formula for the surface area of a square pyramid is given by: Surface Area = (Area of Base) + Lateral Area. The area of a square base is s^2. Therefore, we can rewrite the formula as: 182 = s^2 + 118.
Now we have a system of equations:
118 = 4s * l / 2
182 = s^2 + 118
Solving these equations will give us the values of 's' and 'l'.