Solution:
Given:
A composite figure showing a square-based pyramid, a square prism, and a cube.
To get the surface area, we find the surface area of each part separately.
For the square-based pyramid,
[tex]\begin{gathered} It\text{ has four triangles and a square base.} \\ \text{The square base is not part of the surface of the whole shape however.} \\ \\ \text{Hence, the area of the pyramid is;} \\ 4\times\text{area of triangle} \\ b=6 \\ h=4 \\ A=\frac{1}{2}bh \\ \text{Hence,} \\ \text{Area}=4\times\frac{1}{2}\times6\times4=48 \\ A=48ft^2 \end{gathered}[/tex]
The surface area of the pyramid is 48 square feet.
For the square prism,
It has 6 faces. However, only four are the surface of the composite shape. The other two faces are inside the shape and will not count as a surface.
Hence,
[tex]\begin{gathered} \text{Area of front and back face;} \\ A=l\times b \\ A=20\times6=120 \\ \text{For the two faces;} \\ A=2\times120=240ft^2 \\ \\ \text{Also, the area of the top and bottom face,} \\ A=20\times6=120 \\ \text{For the two faces;} \\ A=2\times120=240ft^2 \\ \\ \text{Hence, the surface area of the square prism is 240+240} \\ =480ft^2 \end{gathered}[/tex]
Therefore, the area of the square prism is 480 square feet.
For the cube;
The cube has 6 faces.
However, only 5faces are part of the surface of the composite shape. One face is within the shape.
Hence,
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