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