The surface area of a square pyramid whose base area is 196 square inches and the height of each of its triangular faces is 16 inches is 685 in².
What is surface area?
Surface area of any solid or the 3 dimensional body is the area of each faces by which the solid body is enclosed.
The surface area of a square pyramid is calculated with the following formula.
[tex]A_s=a^2+2a\sqrt{\dfrac{a^2}{4}+h^2}[/tex]
Here, (h) is the height of the pyramid and (a) is the side of the base.
The square pyramid has a base area equal to 196 square inches. Thus, the length of its side is,
[tex]A=a^2\\196=a^2\\14^2=a^2\\14=a[/tex]
Thus, the side of the base is 14 in. The height of each of its triangular faces is 16 inches. Put these values in the above formula as,
[tex]A_s=(14)^2+2(14)\sqrt{\dfrac{(14)^2}{4}+(16)^2}\\A_s=684.999\\A_s\approx 685 \rm in^2[/tex]
Hence, the surface area of a square pyramid whose base area is 196 square inches and the height of each of its triangular faces is 16 inches is 685 in².
Learn more about the surface area here:
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