How to Calculate the Area and Diagonals of a Rhombus
To find the area of a rhombus, you can use the following formulas:
- Area based on side length and altitude: Area = Side × Altitude
- Area based on diagonals: Area = (Diagonal 1 × Diagonal 2) / 2
Calculating the Area
Given that the side length of the rhombus is 5 cm and the altitude is 4 cm, you can calculate the area as follows:
Area = 5 cm × 4 cm = 20 cm²
Finding the Length of the Other Diagonal
We know one of the diagonals is 8 cm, and we can use the area found earlier to find the other diagonal. Using the area formula based on the diagonals:
Area = (Diagonal 1 × Diagonal 2) / 2
Let’s set Diagonal 1 = 8 cm and let Diagonal 2 = d. Substituting the values into the area formula gives:
20 cm² = (8 cm × d) / 2
Multiplying both sides by 2 to eliminate the fraction:
40 cm² = 8 cm × d
Now, divide both sides by 8 cm to solve for d:
d = 40 cm² / 8 cm = 5 cm
Final Results
In summary, the following results hold:
- Area of the rhombus: 20 cm²
- Length of the other diagonal: 5 cm
So, to recap, with a side length of 5 cm and an altitude of 4 cm, the area of the rhombus is 20 cm², and the length of the other diagonal is 5 cm.