Question

Please help me with the question below (also please explain).

Answer 1

Determining the faces of the figure, we have the following:

1 and 2 are square surfaces with dimensions 10ft by 10 ft

3,4 and 9 are rectangle surfaces with dimensions 10ft by 14ft

5 and 6 are triangle surfaces with height 8 ft, and base 10 ft

8 and 7 are rectangle surfaces with dimensions 9ft by 14ft.

We have the following formula to solve for the surface area.

`\begin{gathered} SA=2(10\text{ ft})(10\text{ ft})+3(10\text{ ft})(14\text{ ft})+2\cdot(1)/(2)(8\text{ ft})(10\text{ ft})+2(9\text{ ft})(14\text{ ft}) \\ SA=2(100\text{ ft}^2)+3(140\text{ ft}^2)+2(40\text{ ft}^2)+2(126\text{ ft}^2) \\ SA=200\text{ ft}^2+420\text{ ft}^2+80\text{ ft}^2+252\text{ ft}^2 \\ SA=952\text{ ft}^2 \end{gathered}`

Therefore, the surface are of the given figure is 952 square feet.