Given:
• Length of base(cube) = 6 ft
,• Height of square prism = 20 ft
,• Height of pyramid =4 ft
Since it is a composite figure, the surface of some sides will not be included in the surface area.
Let's solve for the following:
• (a). The surface area of the pyramid.
To find the surface area of the pyramid, apply the formula:
[tex]SA=A+\frac{1}{2}ps[/tex]Where:
A is the area of the base
p is the perimeter of the base
s is the slant height.
To find the slant height, apply Pythagorean theorem:
[tex]\begin{gathered} s=\sqrt{(4)^2+(\frac{6}{2})^2} \\ \\ s=\sqrt{16+9}=\sqrt{25}=5\text{ ft} \end{gathered}[/tex]We have:
[tex]\begin{gathered} SA=(6*6)+\frac{1}{2}(6*4)*5 \\ \\ SA=36+\frac{1}{2}(24)*5 \\ \\ SA=36+60 \\ \\ SA=96\text{ ft}^2 \end{gathered}[/tex]The surface area of the pyramid is 96 ft².
• (b). Surface area of the square prism.
Apply the formula:
[tex]\begin{gathered} SA=3ah \\ \\ SA=4(6)(20) \\ \\ SA=480\text{ ft}^2 \end{gathered}[/tex]The surface area of the square prism is 480 ft².
• (c). Surface area of the cube.
To find the surface area of the cube, we have:
[tex]\begin{gathered} SA=6a^2 \\ \\ SA=6(6)^2 \\ \\ SA=216\text{ ft}^2 \end{gathered}[/tex]The surface area of the cube is 216 ft²
The total surface area will be:
T = Surface area of pyramid + surface area of prism + surface area of cube - area of base
T = 96 + 480 + 216 - 36
T = 756 ft²
ANSWER:
Surface area of the pyramid is 96 ft².
Surface area of the square prism is 480 ft².
Surface area of the cube is 216 ft²
Total surface area is 756 ft²