Let's find the surface area of the composite figure shown.
The top of the figure is a square base pyramid while the bottom is a square prism.
To find the surface area of the composite figure, find the surface area of the square base pyramid and the surface area of the square prism.
To find the surface area of the square pyramid, apply the formula:
[tex]SA=a^2+2al[/tex]Where:
a = 15 ft
l is the slant height = 9ft
Thus, we have:
[tex]\begin{gathered} SA=15^2+2(15)(9) \\ \\ SA=225+270 \\ \\ SA=495ft^2^{} \end{gathered}[/tex]The surface area of the square pyramid is 495 square feet.
Now, let's find the area of the square prism.
Apply the formula:
[tex]SA=2a^2+4ah[/tex]Where:
a = 15 ft
h = 15 ft
We have:
[tex]\begin{gathered} SA=2(15)^2+4(15)(15) \\ \\ SA=2(225)+4(225) \\ \\ SA=450+900 \\ \\ SA=1350ft^2 \end{gathered}[/tex]The surface area of the square prism is 1350 square feet.
To find the surface area of the composite figure, add the area of the square pyramid and square prism.
We have:
Surface area = 495 square feet + 1350 square feet = 1845 square feet.
Therefore, the surface area of the compposite figure is 1845 square feet.
ANSWER:
1845 sqaure feet.