Final answer:
The area of the rhombus is calculated as 96 square cm by using the known perimeter to find the length of the sides, using Pythagoras' theorem to find the length of the unknown diagonal, and applying these values in the formula for the area of a rhombus.
Step-by-step explanation:
The perimeter of a rhombus is equal to 4 times the length of one side. If the perimeter is 40 cm, each side of the rhombus is therefore 40 / 4 = 10 cm. The area of a rhombus can be calculated using the formula: area = 1/2 * d1 * d2, where d1 and d2 are the lengths of the diagonals.
If we know the length of one diagonal (16 cm), we can use the property of the rhombus that the diagonals are perpendicular bisectors of each other.
Hence, the second diagonal can be calculated by using Pythagoras' theorem: d2 = sqrt(s^2 - (0.5*d1)^2), where s is the length of one side. Substituting our known values,
we find d2 = sqrt(10^2 - (0.5*16)^2) = 12 cm.
Substituting these values into our area formula, we find that the area of the rhombus is 1/2 * 16 cm * 12 cm = 96 cm^2.
Learn more about Area of Rhombus