Answer:
The total surface area is [tex]251\ cm^{2}[/tex]
Step-by-step explanation:
we know that
The total surface area of the composite figure is equal to the lateral area of the pyramid plus the lateral area of the cube plus the area of the base of the cube
The lateral area of the pyramid is equal to the area of the four lateral triangular faces of the pyramid
The lateral area of the cube is equal to the area of the four lateral square faces of the cube
so
[tex]SA=4[\frac{1}{2}(b)(h)]+4(b^{2})+b^{2}[/tex]
we have that
[tex]b=6\ cm[/tex]
[tex]h=5.9\ cm[/tex]
substitute
[tex]SA=4[\frac{1}{2}(6)(5.9)]+4(6^{2})+6^{2}[/tex]
[tex]SA=70.8+144+36[/tex]
[tex]SA=250.8\ cm^{2}[/tex]
Round to the nearest square centimeters
[tex]250.8=251\ cm^{2}[/tex]
