Question

how do i find surface area for a square pyramid? the base is 3ft each side and 6ft on the side going up. ive tried reading over my lessons so many times and I just cant figure out how to do it.

Answer 1

the base is square so its area is just 3^2 = 9

If by "on the side going up" you mean the slant height, then the lateral faces are just four triangles with a base of 3 and a height of 6, so their area is 4(1/2 * 3 * 6) = 36

This is what the bot calculated.

If by "on the side going up" you mean the length of the edge where the faces meet, then if you draw a side view, you can see that the height h of the pyramid can be found using
h^2 + (3/2 √2)^2 = 6^2
h^2 + 9/2 = 36
Then the slant height s can be found using
s^2 = (3/2)^2 + h^2 = (3/2)^2 + (36 - 9/2) = 33.75
s = √135/2
and the lateral area is 4 * 1/2 * 3 * √135/2 = 3√135