Given:
The height of the pyramid is h = 3ft
The base of the pyramid is square.
The side of the square is a =16 ft.
Required:
We need to find the surface area of the pyramid.
Explanation:
Consider the surface area of the pyramid formula.
[tex]S=base\text{ area+}\frac{1}{2}\times perimeter\times slant\text{ height.}[/tex][tex]Substitute\text{ base area=a}^2,\text{ perimeter =4a since the base is square. and let slant height =l.}[/tex][tex]S=a^2\text{+}\frac{1}{2}\times4a\times l[/tex]
Use the Pythagorean theorem to find the slant height l.
[tex]l=\sqrt{3^2+8^2}[/tex][tex]l=\sqrt{9+64}[/tex][tex]l=\sqrt{73}[/tex]
[tex]S=a^2\text{+}\frac{1}{2}\times4a\times l[/tex][tex]Substitute\text{ a =16 and l=}\sqrt{73}\text{ in the formula.}[/tex][tex]S=16^2\text{+}\frac{1}{2}\times4(16)\times\sqrt{73}[/tex][tex]S=256+32\sqrt{73}[/tex][tex]S=32(8+\sqrt{73})ft^2[/tex]
Final answer:
The surface area of the given pyramid is
[tex]S=32(8+\sqrt{73})ft^2[/tex]
