Question

A right square pyramid has a height h and a base that is s units on each side. the slant height is twice the pyramid's height. which expression represents the surface area of the pyramid in terms of h?

Answer 1

The answer to this question is:

A right square pyramid has a height h and a base that is s units on each side. the slant height is twice the pyramid's height. which expression represents the surface area of the pyramid in terms of h?"4hs + s^2"

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Answer 2

surface area of the pyramid in terms of h
`s^2+4hs`

Explanation:

Surface area of pyramid(S) is given by:

`S = \text{Base area}+\text{Lateral Area}`

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 =
`s^2` square units.

It is also given that: the slant height is twice the pyramid's height

⇒
`\text{Slant height} = 2h`

`\text{Lateral area} = (1)/(2) \text{Perimeter of the base} * \text{Slant height}`

Substitute the given values we have;

`\text{Lateral area} = (1)/(2)(4s)(2h) = 4sh`

then:

Surface area of pyramid is:

`S = s^2+4hs` where s is the side and h is the height of the pyramid.

Therefore, surface area of the pyramid in terms of h
`s^2+4hs`