Answer:
V = 120.6796
LA = 110.8513
SA = 174.8513
Step-by-step explanation:
Let me know if you need more of an explanation for any of these
First we need the height, one way to find that out is to use the diagonal of the and one of the diagonal edges of the pyramid. Specifically we will need half of the diagonal of the square. We will call the diagonal of the square d.
Gonna leave it like that for ease of writing. So then half of the diagonal is
The height, h, will be . Plugging everything in gets us
last, we need to find slant height, which we will call s.
s is also the height of the triangles for purposes of finding area. Now for the volume and areas.
Volume is area of the base times height divided by 3, so
Lateral area is the sum of the four areas of the triangles, and each of those are so the whole lateral area is 4 times that. So we get
Total surface area is the lateral surface area + the area of the base, so 110.8513 + 64 = 174.8513