The total surface area of a regular square pyramid having slant height of 10units and base length of 6 units is 168 square inches which is fifth option.
Given that slant height is 10 units and base lengths of 6 units.
We are required to calculate total surface area of regular square pyramid.
We know that total surface area of regular square based pyramid is equal to [tex]s^{2} +s\sqrt{s^{2} +4h^{2} }[/tex] in which s is side of base length and h is slant height of regular square pyramid.
Total surface area=[tex]6^{2} +6\sqrt{6^{2} +4*10^{2} }[/tex]
=36+6[tex]\sqrt{36+400}[/tex]
=36+6[tex]\sqrt{436}[/tex]
=36+6*20.88
=36+125.28
=161.28
Nearest option is 168 square inches.
Hence the total surface are of regular square based pyramid is option 5 which is 168 square inches.
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