Buzz
Students have learned about finding the area of a rhombus when knowing the two diagonals. Yet, calculating the area of a rhombus with a known angle poses a relative challenge. To assist students in tackling this task more easily, we've analyzed the problem below for your reference.
Calculating Rhombus Area with Known Angle
Calculating Rhombus Area with Known Angle
Reviewing the Theory of Rhombus Area
Students have been taught how to calculate the area of a rhombus using the formula:
S = 1⁄2 (d
Considering:
S is the area of the rhombus
d1 is the first diagonal
d2 is the second diagonal
- Characteristic angles of a rhombus: Opposite angles are equal.
So, can we calculate the area of a rhombus when the angle is known?
As you know, the area of a rhombus is equal to half the product of the lengths of its diagonals, so knowing only an angle is insufficient for calculations. When the angle is known, we need an additional condition about the side to determine the area. So, how do we calculate the area of a rhombus with a known angle and side?
* Here is a problem: Calculate the area of rhombus ABCD given a side length of 6 cm, and one of the angles is 40 degrees.
Instructions:
- From B, drop a perpendicular BH to BD. BH is the height of rhombus ABCD.
- Since rhombus ABCD is also a parallelogram, we can apply the formula: The area of a rhombus is the height multiplied by the base length.
- Knowing the length of one side and angle BAD, we can completely calculate the height BH based on trigonometric ratios in the right-angled triangle.
Solution:
From B, drop BH perpendicular to AD. In the right-angled triangle ABH at H, we have:
So, with the example above, students must have a better understanding of problems related to the formula for calculating the area of a rhombus with a known angle. However, this condition is not sufficient; we need to find one more condition to make the calculation easier. If there's a quicker and more interesting solution, feel free to share it with us.
Additionally, it's crucial for students to comprehend how to calculate the area of a rhombus when all 4 sides are known. This is a common type of rhombus area problem that you may encounter frequently.
