Answer:
The slant height is 6.32 ft ( approx )
Step-by-step explanation:
Since, the slant height formula of a square frustum,
[tex]s=\sqrt{(r_1-r_2)^2+h^2}[/tex]
Where, [tex]r_1[/tex] is apothem of the lower base,
[tex]r_2[/tex] is the apothem of the upper base,
And, h is the altitude,
Given,
The lower base is a square 8 ft on each side,
So, its apothem,
[tex]r_1=\frac{8}{2tan(\frac{180}{4})}=\frac{4}{tan45}=4[/tex]
Similarly,
The upper base is a square 4 ft on each side,
[tex]\implies r_2=\frac{4}{2tan(\frac{180}{4})}=2[/tex]
Also, h = 6 ft,
Hence, the slant height of the given frustum is,
[tex]s=\sqrt{(4-2)^2+6^2}=\sqrt{4+36}= \sqrt{40}=6.32455532034\approx 6.32\text{ ft}[/tex]
