Answer:
6.08 fluid ounces
Explanation:
You want the amount of stain required to cover the surface area of the ends and three sides of a beam 6" square and 6 ft long. 128 floz of stain will cover 200 square feet.
End area
The two ends of the beam are 1/2 ft square, so the area of each is ...
A = s² = (1/2 ft)² = 1/4 ft²
The two ends have a total area of ...
2 × (1/4 ft²) = 1/2 ft² . . . . end area
Side area
Three of the four sides of the beam are to be stained, so their total area is the area of 3 rectangles, each of which is 1/2 ft by 6 ft.
The area of each rectangle is ...
A = LW
So, the area of the three rectangles is ...
total side area = 3 × (1/2 ft)(6 ft) = 9 ft²
Beam area
Then the area to be stained is the sum of the end area and the side area:
stained area = (1/2 ft²) +(9 ft²) = 9.5 ft²
Stain quantity
The amount of stain required is proportional to the area, so we can write the proportion ...
q/(9.5 ft²) = (128 floz)/(200 ft²)
Multiplying by 9.5 ft² gives ...
q = (128 floz)(9.5/200) = 6.08 floz
The homeowner needs 6.08 fluid ounces of stain to stain the beam.