Final answer:
The area of the rhombus is 72 cm² and the perimeter is 48 cm.
Step-by-step explanation:
A rhombus is a quadrilateral with all sides of equal length. In a rhombus, opposite angles are equal. We can use the given information to calculate the area and perimeter of the rhombus.
Calculation of Area:
The area of a rhombus can be calculated using the formula: Area = (diagonal1 * diagonal2) / 2.
Given that the length of the shorter diagonal is 12 cm and the longer diagonal is equal to the shorter diagonal:
Area = (12 * 12) / 2 = 144 / 2 = 72 cm²
Calculation of Perimeter:
The perimeter of a rhombus can be calculated by multiplying the length of one side by 4.
In a rhombus, all sides are equal. Let's say the length of one side is 's' cm:
Perimeter = 4s
We can find 's' using the law of cosines: cos(angle) = (s² + s² - 12²) / (2s * 2s)
cos(60°) = (s² + s² - 12²) / (4s²)
0.5 = (2s² - 144) / (4s²)
2s² - 144 = 0.5 * 4s²
2s² - 144 = 2s²
s² = 144
s = √144 = 12 cm
Perimeter = 4 * 12 = 48 cm