Question

Mr. Williams is painting only the back of his barn. A gallon of paint covers 70 square feet. How many square feet will Mr. Williams be painting? How many gallons of paint does he need to buy? A) 264 ft2; 4 gallons B) 264 ft2; 3 gallons C) 276 ft2; 4 gallons D) 276 ft2; 3 gallons Submit Hint Calc Geometry (MGSE6.G.1) Find Area ID: 106377

Answer 1

A) 264
`ft^2`; 4 gallons

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 =
`Length* Width= 18\ft* 12\ ft = 216\ ft^2`

The height of the triangle can be calculated as =
`28\ ft- 18\ ft=10\ ft`

Area of triangle =
`(1)/(2)* base* height=(1)/(2)* 12\ ft* 10\ ft = 60\ ft^2`

Area of the rectangular window =
`Length* Width= 4\ft* 3\ ft = 12\ ft^2`

Thus, the area that needs to be painted would be :

⇒
`216\ ft^2+60\ ft^2-12\ ft^2`

⇒
`264\ ft^2` (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 =
`(264)/(70)=3.77\approx 4` gallons (Answer)

Thus, Mr. Williams needs to buy 4 gallons of paint to paint 264 square feet of his barn.