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

Answer:

$10\frac{5}{12}$  sq. meters

Step-by-step explanation:

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

Area of Wall =  $2\frac{1}{2}*5\frac{1}{2}=\frac{5}{2}*\frac{11}{2}=\frac{55}{4}$

1 painting area is  $1\frac{1}{4}*\frac{2}{3}=\frac{5}{4}*\frac{2}{3}=\frac{10}{12}$

Thus, 4 of them have area  =   $4*\frac{10}{12}=\frac{40}{12}$

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

Area NOT COVERED =  $\frac{55}{4}-\frac{40}{12}\\=\frac{55(3)-40}{12}=\frac{125}{12}=10\frac{5}{12}$

Thus  $10\frac{5}{12}$  sq. m. is NOT COVERED