Answer:
The area of the pyramid’s base is 36 in².
The pyramid has 4 lateral faces.
The surface area of each lateral face is 27 in².
Step-by-step explanation:
"Lateral" means side, so the lateral faces are triangles.
The base is the bottom, which is a square.
To calculate the area of the base, use the formula for area of a square.
[tex]A_{base} = s^{2}[/tex]
[tex]A_{base} = (6 in)^{2}[/tex]
[tex]A_{base} = 36 in^{2}[/tex]
To calculate the area of a lateral face, find the area of a triangle.
[tex]A_{lateral} = \frac{bh}{2}[/tex]
[tex]A_{lateral} = \frac{(6 in)(9 in)}{2}[/tex]
[tex]A_{lateral} = \frac{54 in^{2}}{2}[/tex]
[tex]A_{lateral} = 27 in^{2}[/tex]
In a pyramid, the number of lateral faces is the same as the number of sides in the base. The square base as 4 sides, so there are 4 lateral faces.
