A detailed diagram of a pyramid with a square base. The pyramid should be placed on a coordinate grid system for added clarity. To visually demonstrate the measurements of the pyramid, the sides of the base should be clearly labelled as 7.8 cm. The height of the pyramid, from the vertex to the center of the base, should also be accurately indicated as 9.3 cm. The slant edge should be highlighted with a different color and its length left uncalculated. Additional arrows and markers should be used to further clarify the different dimensions and aspects of the pyramid.

Calculate the length of the slant edge and the total surface area of the pyramid square base 7.8 cm and height 9.3 cm

If you look at your sketch you will see that we need the diagonal of

the base first of all.
let that diagonal be d
d^2 = 7.8^2 + 7.8^2
d = appr. 11.0309
so half of that is 5.51543...
let the slant edge be s
s^2 = 5.51543..^2 + 9.3^2
s = 10.812 cm

for the surface area, just find the area of one of the 4 identical
triangles, then multiply by 4

We need the height of one of those triangles.
Again look at your sketch, label that height as h
h^2 = ( (1/2)(7.8) )^2 + 9.3^2
h = 10.0846

area of 1 triangle = (1/2)(base)(height)
= (1/2)(7.8)(10.0846) = 39.330...

so total lateral surface area = 4(39.330..) cm^2 = 157.32 cm^2

check my arithmetic, I will leave it up to you to decide if the
surface area of the base should be included. If so, just add 7.8^2