To find the surface area of a square pyramid, you need to use the formula SA = B + 1/2P(L + S), where B is the area of the base, P is the perimeter of the base, L is the slant length of the pyramid, and S is the length of the side of the pyramid.
In this case, the base is a square with sides of 3ft, so the area of the base is 9ft^2. The perimeter of the base is 12ft. The slant length of the pyramid is 6ft, and the length of the side of the pyramid is also 6ft.
Plugging these values into the formula, we get SA = 9 + 1/2(12)(6 + 6) = 9 + 36 = 45ft^2.
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.
2 answers
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
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