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?
wall area: 2.5m * 5.5m = 13.75 m^2
paintings: 4*1.25*2/3 = 3.33 m^2
so, what's the difference?
10.42
To find the area of the wall that is not covered by paintings, we need to calculate the total area of the wall and subtract the combined area of the four paintings.
First, let's convert the dimensions to a common unit. Both the wall and the paintings are given in meters, so we'll use meters as the unit.
The height of the wall is 2 1/2 meters. To add it up, we have:
2 meters (whole number part) + 1/2 meter (fraction part) = 2.5 meters
The width of the wall is 5 1/2 meters. Similarly,
5 meters (whole number part) + 1/2 meter (fraction part) = 5.5 meters
Next, we calculate the area of each painting:
Height: 1 1/4 meters
Width: 2/3 meter
To find the area of a rectangle, we multiply its length by its width. Therefore, the area of each painting is:
(1 1/4) meters * (2/3) meter = (5/4) meters * (2/3) meter = (10/12) meters * (8/12) meters = 80/144 square meters
Since there are four identical paintings, the combined total area of the paintings is:
4 * (80/144) square meters = (320/144) square meters = 2.22 square meters (rounded to two decimal places)
Now, we can find the area of the wall that is not covered by paintings:
Total wall area = height * width = 2.5 meters * 5.5 meters = 13.75 square meters
Remaining area = Total wall area - Combined area of paintings = 13.75 square meters - 2.22 square meters = 11.53 square meters
Therefore, the area of the wall that is not covered by paintings is approximately 11.53 square meters.