Answer:
The surface area is [tex]288\ cm^{2}[/tex]
Step-by-step explanation:
we know that
The surface area of the square pyramid is equal to the area of the square base plus the area of its four triangular lateral faces
so
[tex]SA=b^{2} +4[(\frac{1}{2}) (b)(h)][/tex]
where
b is the length side of the square base
h is the height of each lateral triangular face
we know that
[tex]\frac{b}{2}=h[/tex] -----> by angle of 45 degrees
[tex]sin(45\°)=\frac{h}{6\sqrt{2}}[/tex]
[tex]h=6\sqrt{2}(sin(45\°)[/tex]
[tex]h=6\ cm[/tex]
Find the value of b
[tex]b=2h=2(6)=12\ cm[/tex]
Find the surface area
[tex]SA=12^{2} +4[(\frac{1}{2}) (12)(6)]=288\ cm^{2}[/tex]
