Answer:
surface area of the pyramid in terms of h [tex]s^2+4hs[/tex]
Step-by-step explanation:
Surface area of pyramid(S) is given by:
[tex]S = \text{Base area}+\text{Lateral Area}[/tex]
As per the statement:
A right square pyramid has a height h and a base that is s units on each side.
Base area of square = [tex]s^2[/tex] square units.
It is also given that: the slant height is twice the pyramid's height
⇒[tex]\text{Slant height} = 2h[/tex]
[tex]\text{Lateral area} = \frac{1}{2} \text{Perimeter of the base} \times \text{Slant height}[/tex]
Substitute the given values we have;
[tex]\text{Lateral area} = \frac{1}{2}(4s)(2h) = 4sh[/tex]
then:
Surface area of pyramid is:
[tex]S = s^2+4hs[/tex] where s is the side and h is the height of the pyramid.
Therefore, surface area of the pyramid in terms of h [tex]s^2+4hs[/tex]
