Answer:
A) 264 [tex]ft^2[/tex]; 4 gallons
Step-by-step explanation:
The figure for the question is shown below.
Given:
Mr. William is painting only the back of his barn.
A gallon of paint covers 70 square feet.
To find how many square feet will Mr. William be painting and how many gallons of paint does he need to buy.
Solution:
From the given figure, we can find the square feet of yarn that needs to be painted as following:
⇒ Area of the rectangle + Area of the triangle - Area of the rectangular window.
Area of rectangle = [tex]Length\times Width= 18\ft\times 12\ ft = 216\ ft^2[/tex]
The height of the triangle can be calculated as = [tex]28\ ft- 18\ ft=10\ ft[/tex]
Area of triangle = [tex]\frac{1}{2}\times base\times height=\frac{1}{2}\times 12\ ft\times 10\ ft = 60\ ft^2[/tex]
Area of the rectangular window = [tex]Length\times Width= 4\ft\times 3\ ft = 12\ ft^2[/tex]
Thus, the area that needs to be painted would be :
⇒ [tex]216\ ft^2+60\ ft^2-12\ ft^2[/tex]
⇒ [tex]264\ ft^2[/tex] (Answer)
Using unitary method:
If 70 square feet is covered by 1 gallon of paint.
Then for 264 square feet, number of gallons of paint required will be = [tex]\frac{264}{70}=3.77\approx 4[/tex] gallons (Answer)
Thus, Mr. Williams needs to buy 4 gallons of paint to paint 264 square feet of his barn.
