Can you please help with this geometry question?

Question

Lily is painting the wall of her house. The wall is rectangular, 15 by 10 feet. There is a door and a window on the wall. The door is rectangular, 3.5 by 6.5 feet. The window is also rectangular, 3 by 6.25 feet. If every square feet of wall space requires one gallon of paint, how many gallons does Lily need to paint her wall?

Answer 1

Hi Deinonychus!

This problem is five steps.

First. You have to find the surface area of the wall in total. It's a rectangle -- the formula for the area of a rectangle is LENGTH times WIDTH. 15 x 10 = 150. So, the wall is 150 sq. ft. in total.

Second. We have to find the surface area of the door. It's also a rectangle so the formula is the same. 3.5 x 6.5 = 22.75. The surface area of the door is 22.75 sq. ft.

Third. We have to find the surface area of the window. Again, we use the same formula because it's a rectangle. 3 x 6.35 = 18.75. This means the surface area of the window is 18.75 sq. ft.

Fourth. Almost done! We have to put this all together to find the area of the wall that can be painted -- meaning we need to SUBTRACT the area of the window and the area of the door from the total area of the wall. So, the equation is 150 - 22.75 - 18.75 = 108.5. Our answer -- 108.5 sq. ft. -- is the amount of wall that can be painted.

Fifth. The last step! Finally, we can figure out how much paint Lily needs. We can do this by re-reading how much paint each square foot needs. The problem says 1 gallon per square foot. The paint-able wall is 108.5 square feet so that means Lily needs 108.5 gallons of paint!

I hope this helped :)

Answer 2

The wall is 10 ft by 15 ft = 150 ft^2

the door is 3.5 ft by 6.5 ft = 22.75 ft^2

the window 3 ft by 6.25 ft = 18.75 ft^2

The remaining wall is 150 ft^2 - 22.75 ft^2 -18.75 ft^2 = 108.5 ft^2

Given that there is 108.5 ft^2 left blank, Lily needs 108.5 gallons of paint.