Question

Hershel is designing a square pyramid that needs to have a lateral surface of 440 in². The area of the base is 121 in². Find the length of the slant height of the pyramid.

Answer 1

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

                                                     $A=\frac{1}{2}pl$

where $p$ represents the perimeter of the base and $l$ 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 $A=s^2$, where s is the length of any side and the perimeter of a square is given by $p=4s$.

Applying the formula for the area of a square we can find the length of the side

$121=s^2\\s^2=121\\s=\sqrt{121}=11$

The perimeter of the base is

$p=4\cdot(11)=44$

Next, we can apply the formula for the lateral surface area and solve for $l$ the slant height.

$440=\frac{1}{2}44l\\\\\frac{1}{2}\cdot \:44l=440\\\\22l=440\\\\l=20$

The length of the slant height of the square pyramid is 20 in.