Answer:
[tex]36+15+15+15+15[/tex]
Step-by-step explanation:
For the surface area we need to add up all the areas in the pyramid:
- area of the triangle sides (there are 4 triangles)
Area of the base:
the base is a square, and the area of a square is given by:
[tex]a_{base}=l^2[/tex]
where [tex]l[/tex] is the length of the side: [tex]l=6[/tex], thus:
[tex]a_{base}=(6)^2\\a_{base}=36[/tex]
Area of the triangles:
one triangle has the area given by the formula:
[tex]a_{triangle}=\frac{b*h}{2}[/tex]
where [tex]b[/tex] is the base of the triangle: [tex]b=6[/tex]
and [tex]h[/tex] is the height of the triangle: [tex]h=5[/tex], thus we have the following:
[tex]a_{triangle}=\frac{6*5}{2} \\\\a_{triangle}=\frac{30}{2} \\\\a_{triangle}=15[/tex]
the expression that represents the surface area of the pyramid is:
[tex]a_{base}+area_{triangle}+area_{triangle}+area_{triangle}+area_{triangle}[/tex]
substituting our values:
[tex]36+15+15+15+15[/tex]
which is option B
