Finding Slant Height from Surface Area and Base Length

[ODB123]

Hello. I am stuck on a basic junior high/high school math problem. We are asked to find the slant height of a regular pyramid (apex directly above base) and are given the surface area and the measurement for the length of the base. I believe I would use Pythagorean theorem to solve this but I am unsure. How would I go about solving this?

SA=50.75in squared
Side Length=3.5"

Help is greatly appreciated as I am stuck on this.

 

[Deleted member 4993]

Hello. I am stuck on a basic junior high/high school math problem. We are asked to find the slant height of a regular pyramid (apex directly above base) and are given the surface area and the measurement for the length of the base. I believe I would use Pythagorean theorem to solve this but I am unsure. How would I go about solving this?

SA=50.75in squared
Side Length=3.5"

Help is greatly appreciated as I am stuck on this.

Is there a picture associated with this problem? I think:

The pyramid in question is a square with four slant faces.

Please post the EXACT problem given to you along with any relevant sketches.

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

https://www.freemathhelp.com/forum/threads/read-before-posting.109846/#post-486520

 

[Dr.Peterson]

Can you find a formula for the surface area of a regular pyramid?

Is the surface area in the problem the total area, or the lateral area? Is this a square pyramid?

 

[ODB123]

I think I figured it out. It was easier than I thought it was. Thank you for your help!

Key was just using formula for pyramid (SA=LW+LS+WS) with "S" standing for "slant"

Question was: Find slant using base and total surface area of square pyramid.

 

[Dr.Peterson]

Yes, that's the idea. There is a more general formula for any right pyramid, and a more specific one for a regular polygon or square pyramid, but your formula is good.

Quite often my question, "Can you find a formula [relating those quantities]?" is a key step in problem solving. Other times, there's no formula, but you can write your own equations. But discovering what tools you have available is a big chunk of the work.