Answer:
Optión C. [tex]550\ ft^2[/tex]
Step-by-step explanation:
1. The surface area of the complex figure is the sum of the surface area of 5 of the faces of both cubes and the surface area of 5 of the faces of the rectangular prism.
2. The formula to calculate the surface area of one of the faces of a cube is:
[tex]A_c = L ^ 2[/tex]
where L is the length or width of the face.
We must calculate the area of 5 of the faces for both cubes, since the area of the lower face is not part of the figure.
[tex]A_c = 10L ^ 2[/tex]
[tex]A_c = 10(5\ ft) ^2\\\\A_c = 250\ ft ^2[/tex]
3. The formula for calculating the surface area of a rectangular prism is
[tex]A_p = 2Lh +2Lw +2wh[/tex]
Where
L = length
h = height
w = width
In this case we should not calculate the area of the entire upper face of the rectangular prism, but only the area of the square whose side is 5 ft that is in the middle of the figure. Then we subtract [tex]\frac{2}{3}Lw[/tex] from the formula and we have left:
[tex]A_p = 2Lh + \frac{4}{3}Lw + 2wh\\\\A_p = 2 (15\ ft)(5\ ft) + \frac{4}{3}(15\ ft)(5\ ft) + 2(5\ ft)(5\ ft)[/tex]
[tex]A_p = 300[/tex]
4. Therefore, the surface area of the complex figure is:
[tex]A = A_p + A_c\\\\A = 300 + 250\\\\A = 550\ ft^2[/tex]
The correct answer is option C.
