Answer:
The length of the slant height of the square pyramid is 20 in.
Step-by-step explanation:
The lateral surface area of a regular pyramid is the sum of the areas of its lateral faces.
The general formula for the lateral surface area of a regular pyramid is
[tex]A=\frac{1}{2}pl[/tex]
where [tex]p[/tex] represents the perimeter of the base and [tex]l[/tex] the slant height.
From the information given we know that:
- The lateral surface area of a square pyramid is 440 in².
- The area of the base is 121 in².
And we want to find the the slant height of the pyramid.
For this, we also need to know that the area of a square is given by [tex]A=s^2[/tex], where s is the length of any side and the perimeter of a square is given by [tex]p=4s[/tex].
Applying the formula for the area of a square we can find the length of the side
[tex]121=s^2\\s^2=121\\s=\sqrt{121}=11[/tex]
The perimeter of the base is
[tex]p=4\cdot(11)=44[/tex]
Next, we can apply the formula for the lateral surface area and solve for [tex]l[/tex] the slant height.
[tex]440=\frac{1}{2}44l\\\\\frac{1}{2}\cdot \:44l=440\\\\22l=440\\\\l=20[/tex]
The length of the slant height of the square pyramid is 20 in.
