A right square pyramid has a surface area of 75.5m^2 and a base length of 3.5m. What is the slant height of this right pyramid?

Clearly the surface area would consist only of the 4 triangles.

area of one of them = 75.5/4 or 18.875 m^2

area = (1/2)base x height
18.875 = (1/2)(3.5)h
h = 2(18.875)/3.5 = appr 10.7857

clean up to whatever accuracy is expected
I would say 10.8 , since the original data had one decimal

but the answer is 9.0 and 10.8 won't work for the other questions :(

define what you mean by slant height.

the height that's not at the center but on the side?

then I am right

check:

area of one triangle = (1/2)(3.5)(10.7857
= 18.875

4 such triangle = 4(18.875) = 75.5

To find the slant height of the right square pyramid, we need to use the surface area and the base length.

First, let's start by determining the lateral surface area of the pyramid. The lateral surface area includes all the triangular faces of the pyramid, excluding the base.

The formula for the lateral surface area of a right square pyramid is given by:
Lateral Surface Area = 4 × (1/2) × base length × slant height

We are given that the surface area is 75.5 m^2 and the base length is 3.5 m. Plugging these values into the formula, we can solve for the slant height:

75.5 = 4 × (1/2) × 3.5 × slant height

To isolate the slant height, divide both sides of the equation by 4 and multiply by 2:

75.5 / 4 × 2 = 3.5 × slant height

37.75 = 3.5 × slant height

Now, divide both sides of the equation by 3.5 to solve for the slant height:

37.75 / 3.5 = slant height

The slant height of the right square pyramid is approximately 10.79 meters.