Question

a square based pyramid with side 18cm and height 12cm, calculate the surface area.

Answer 1

a=2bs + b^2
a=2(18)(6√13) + (18)^2
a = 1102.799076
I searched the formula up online and i did that. idk what to do next.

Answer 2

let us look at the bottom of the SQUARE BASE pyramid

Answer 3

what do you think will be half-way to the center towards the "apothem"?

Answer 4

9?

Answer 5

right, now lemme stand up your pyramid, and let us find the so-called "slant height", using the pythagorean theorem

Answer 6

keep in mind that \(\bf c^2 = a^2 + b^2\)

Answer 7

c^2= a^2 + b^2
c^2 = 12^2 + 9^2
c^2 = 144 +81
c^2 = 225
√c^2= √225
c = 15

Answer 8

yes

Answer 9

so now you have the slant height
and the slant height, which is really the "nose of the triangular face"
is also the height of that triangular face, and the area of a triangle is 1/2 (base)(height)

you have 4 triangular faces, add them all 4
then add to that the Area of the squarish bottom
and that's the area of the pyramid

Answer 10

4(9) +18 = 54?

Answer 11

wait

Answer 12

area of one lateral face = 1/2 (9*15) =67.5
SA = 18 +4(67.5)
SA =288?