Question

the surface area of a pyramid is 85 square meters the side length of the base is 5 meters what is the slant height

Answer 1

6 meters

Explanation:

`A=a^2+2a\sqrt{(a^2)/(4)+h^2}`is the formula that you use

h=vertical altitude and

a=side length of the base

`85=5^2+(2*5)\sqrt{(25)/(4)+h^2}`

`85-25=10\sqrt{(25)/(4)+h^2}`

`(60)/(10)=\sqrt{(25)/(4)+h^2}`

`6=\sqrt{(25)/(4)+h^2}`

`36=(25)/(4)+h^2`

`36-(25)/(4)=h^2`

`36-6.25=h^2`

`29.75=h^2`

Vertical altitude (h) and
`(1)/(2)a` and the slant height form a right triangle with the slant height being the hypotenuse

`h^2+(2.5)^2=s^2`where s=slant height

`29.75+6.25=s^2`

`36=s^2`

s=6 meters

Answer 2

slant height = 6 meters

Explanation:

surface area of pyramid: 2bs + b²

2*5*s + 5² = 85

10s = 85 - 25

10s = 60

s = 6

The slant height is 6 meters.