I don’t understand this

The surface area = 384 units²

Step-by-step explanation:

* Lets explain the square pyramid

- It has a based shaped a square

- It has 5 vertices

- It has 4 triangular side faces

* The surface area of any pyramid is

  1/2 perimeter of the base × slant height + area of the base

∴ Its surface area = (1/2)cl + area of the base, where c is the

  perimeter of the base and l is the slant height and s is the

  side of the base

∵ The base shaped a square

∴ Perimeter of the square is 4s

∴ Area of the square = s²

- We will find the slant height by using Pythagoras theorem

* The slant height is the hypotenuse of the right angled triangle

  whose legs are the height of the pyramid and half the side

  of the square

∴ l = √[h² + (1/2 s)²]

* The surface area = (1/2)cl + s²

∵ s = 12 and h = 8

∴ l = √(8² + 6²) = √(64 + 36) = √100 = 10

∴ c = 4 × 12 = 48

∴ s² = 12² = 144

∴ The surface area = (1/2) × 48 × 10 + 144 = 240 + 144 = 384 units²

* The surface area = 384 units²