A barn is shaped like a rectangular prism with a triangular prism on top as shown. The exterior four walls and two triangular faces need to be repainted. If one gallon of paint covers 232 square feet, how many gallons will it take to repaint the barn?
First, calculate the surface area of the rectangular prism:
Surface Area = 2lw + 2lh + 2wh
Surface Area = 2(30 * 20) + 2(30 * 15) + 2(20 * 15)
Surface Area = 1200 + 900 + 600
Surface Area = 2700 square feet
Next, calculate the surface area of the triangular prism on top:
Surface Area = 2 * (1/2 * base * height) + base * height
Surface Area = 2 * (1/2 * 20 * 15) + 20 * 15
Surface Area = 2 * 150 + 300
Surface Area = 600 square feet
Now, add the surface areas of both prisms to get the total surface area that needs to be painted:
Total Surface Area = 2700 + 600
Total Surface Area = 3300 square feet
Lastly, divide the total surface area by the coverage of one gallon of paint to determine how many gallons are needed:
Gallons needed = 3300 / 232
Gallons needed ≈ 14.22
Therefore, it will take approximately 14.22 gallons of paint to repaint the barn. You will need to round up to the nearest gallon, so you will need 15 gallons of paint to complete the job.