Answer:
The surface area is [tex]180\ m^{2}[/tex]
Step-by-step explanation:
we know that
The surface area of the composite figure is equal to the area of its four lateral triangular faces of the pyramid in the top plus the lateral area of the prism plus the area of the base of the prism
so
[tex]SA=4[\frac{1}{2}(4)(l)]+(4+4+4+4)(8)+4^{2}[/tex]
[tex]SA=8l+144[/tex]
Find the slant height (l) of the pyramid
Applying the Pythagoras Theorem
[tex]l^{2}=(b/2)^{2}+h^{2}[/tex]
we have
[tex]b=4\ m[/tex]
[tex]h=4\ m[/tex]
substitute
[tex]l^{2}=(4/2)^{2}+4^{2}[/tex]
[tex]l^{2}=20[/tex]
[tex]l=\sqrt{20}\ m[/tex]
Find the surface area
[tex]SA=8l+144[/tex]
[tex]SA=8(\sqrt{20})+144=180\ m^{2}[/tex]
