What is the lateral area of a pyramid with given side length and heights?

[vitaly]

This problem is really getting to me, and I don't know why...

INfo: Pyramid, Side length = 300 ft, perpendicular height = 321 ft, and slant height = (work shown later)

1. Find the slant height. Round your answer to the nearest whole number.
(slant height)^2 = (height)^2 + (.5(side))^2
= (321)^2 + (150)^2
(slant height)^2 = 125,541
slant height = 354 feet.

Is that correct?

2. Use your previous answer to find the area of the lateral face.
(I'm not sure if I need to use height or slant height, but I used slant height, because when set straight, the slant height is perpendicular to the base. Please correct me if I'm wrong.)
area = .5(base)(height)
= .5(300)(354)
= 53, 100.

My main concern here is whether to use the slant height (354) or height (321) and why...

Thanks for all the help.

 

[fresh_42]

This is correct. The face is a triangle and you need to use these data. Whether it is a side of another object is irrelevant here. Btw. there is a nice calculator for such things:
https://rechneronline.de/pi/johnson-pyramid.php