Answer:
total surface area (TSA) = [tex]2bs[/tex] + [tex]b^{2}[/tex]
length = 6 mi
slant height = 7 mi
∴ TSA = 2 × 6 × 7 + [tex]6^{2}[/tex]
= 84 + 36
= 120
The surface area of the square pyramid is 120 sq. mi.
Given:
side length (s) = 6 mi
slant height (l) = 7 mi
*image of a typical square pyramid is shown in the attachment below.
Recall:
Formula for surface area of square pyramid (SA) = [tex]A + \frac{1}{2} Pl[/tex]
Where,
[tex]A =[/tex] area of the base = [tex]s^2 = 6^2 = 36[/tex] sq mi
[tex]P =[/tex] perimeter of the base = [tex]4(s) = 4\times 6 = 24[/tex] mi
[tex]l =[/tex] slant height = 7 mi
Plug in the values
[tex]SA = 36 + \frac{1}{2}\times 24\times 7\\SA = 36 +84\\SA = 120[/tex]
The surface area(SA) of the square pyramid is 120 sq. mi
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