a rectangle has a perimeter of 32cm. one side measures 5cm. calculate the area of the rectangle.show your working.
2l + 2w = 32
l + w = 16 , but w = 5 (or l=5, if you prefer)
l+5 = 16
l = 11
area = lw = 11(5) = 55 cm^2
P = 2L + 2W
32 = (2 * 5) + 2W
32 = 10 + 2W
22 = 2W
11 = W
A = LW
A = 5 * 11
A = _______ square centimeters
To calculate the area of a rectangle, we need to know the length of both sides. However, in this case, we only know one side, which measures 5 cm.
Since the perimeter of a rectangle is the sum of all its sides, we can calculate the total length of the other three sides by subtracting the known side from the total perimeter.
Given that the perimeter is 32 cm and we know one side measures 5 cm, we subtract 5 cm from 32 cm to find the sum of the other three sides.
32 cm - 5 cm = 27 cm
Now, we have the sum of the other three sides, which is 27 cm. Since we have two identical sides opposite to each other, we can divide this sum by 2 to find the length of one of those sides.
27 cm ÷ 2 = 13.5 cm
Therefore, the length of one of the other sides is 13.5 cm.
Now, we have the lengths of both sides, so we can calculate the area of the rectangle. The area of a rectangle is given by the formula:
Area = length × width
In this case, the length is 5 cm and the width (the other side) is 13.5 cm. Plugging these values into the formula, we get:
Area = 5 cm × 13.5 cm = 67.5 cm²
Therefore, the area of the rectangle is 67.5 cm².