Answer:
The area of the base is 144 square inches.
The area of each triangular face is 66 square inches.
Grabiel needs 408 square inches of paint.
Step-by-step explanation:
The complete problem is attached.
Notice that the figure is a square pyramid, where its base dimensions are 12 inches by 12 inches, which represents an area of
[tex]B=12 \times 12 = 144 \ in^{2}[/tex]
The slant height of the pyramid is 11 inches, which allow us to find the area of each triangle face
[tex]A=\frac{1}{2}bh =\frac{1}{2}(12)(11)= 66 \ in^{2}[/tex]
But there are four triangle faces, so [tex]A_{faces} =4(66)=264 \ in^{2}[/tex].
Therefore, the area of each triangular face is 66 square inches.
So, the total surface area would be the sum
[tex]S=144+264=408 \ in^{2}[/tex]
Therefore, Gabriel needs 408 square inches to paint the whole model.
