Question

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

Answer 1

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