Question

Can someone please help me with this question and show the steps?

Answer 1

Answer:

$D. \ 408in^2$

Step-by-step explanation:

This is a square pyramid because it's a solid having a square base. The point up the pyramid is called the apex and is directly above the middle of the square base. The surface area of a solid is the total area of its outer surface. If we unfold this pyramid, we'll get one square and four identical triangles. So the surface are can be calculated as follows:

$s=s_{square}+4s_{triangle}$

FOR THE SQUARE:

$s_{square}=L^2 \\ \\ L=12in \\ \\ s_{square}=12^2=144in^2$

FOR THE TRIANGLE:

$s_{triangle}=\frac{bh}{2} \\ \\ b=12in \\ h=11in \\ \\ s_{triangle}=\frac{12\times 11}{2}=66in^2$

Finally:

$s=s_{square}+4s_{triangle} \\ \\ s=144+4(66) \\ \\ s=144+264 \\ \\ \boxed{s=408in^2}$