Question

Peter wants to hang his paintings on a wall that is 2 1/2 meters high and 5 1/2 meters wide. He hangs four paintings each of which is 1 1/4 meters high and 2/3 meter wide. What area of the wall is not covered by paintings?

Answer 1

`10(5)/(12)` sq. meters

Explanation:

The area of the wall is height * width, so:

Area of Wall =
`2(1)/(2)*5(1)/(2)=(5)/(2)*(11)/(2)=(55)/(4)`

1 painting area is
`1(1)/(4)*(2)/(3)=(5)/(4)*(2)/(3)=(10)/(12)`

Thus, 4 of them have area =
`4*(10)/(12)=(40)/(12)`

Area NOT COVERED = Area of Wall - Area of 4 paintings together

Area NOT COVERED =
`(55)/(4)-(40)/(12)\\=(55(3)-40)/(12)=(125)/(12)=10(5)/(12)`

Thus
`10(5)/(12)` sq. m. is NOT COVERED