Understanding the Area of an Equilateral Triangle
To find the area of an equilateral triangle with each side measuring x cm, we can use a specific formula derived from geometry principles. An equilateral triangle has all three sides equal and all three angles equal to 60 degrees.
Formula for Area
The area (A) of an equilateral triangle can be calculated using the formula:
A = (√3 / 4) * x²
This formula arises from the basic properties of triangles and their height.
Steps to Calculate the Area
- Identify the side length: Let the length of each side of the triangle be x cm.
- Apply the formula: Substitute the value of x into the area formula:
A = (√3 / 4) * x²
- Calculate the area: Perform the multiplication to find the area in square centimeters.
Example Calculation
If x = 4 cm:
- Substitute into the formula:
A = (√3 / 4) * (4)²
- Calculate:
A = (√3 / 4) * 16
A ≈ 6.93 cm² (using √3 ≈ 1.732)
Conclusion
The area of an equilateral triangle with side length x can be swiftly calculated using the formula provided. Understanding this concept is essential for solving various problems in geometry and can enhance your mathematical skills. To practice more, refer to resources like EduRev for exercises and explanations.