Area of a triangle with 3 equal sides.
Understand the Problem
The question is asking for the area of an equilateral triangle, which has three equal sides. To find the area, we can use the formula for the area of an equilateral triangle, which involves the length of the sides.
Answer
The area of the equilateral triangle is \( A = 9\sqrt{3} \).
Answer for screen readers
The area of the equilateral triangle is ( A = 9\sqrt{3} ).
Steps to Solve
- Identify the formula for the area of an equilateral triangle
The formula to calculate the area $A$ of an equilateral triangle with side length $s$ is given by:
$$ A = \frac{\sqrt{3}}{4} s^2 $$
- Plug in the value of the side length
If you know the length of the side $s$, substitute it into the formula. For example, if $s = 6$, then calculate:
$$ A = \frac{\sqrt{3}}{4} (6)^2 $$
- Calculate the area
Perform the calculation step by step:
Calculate $6^2 = 36$.
Now substitute this value back into the formula:
$$ A = \frac{\sqrt{3}}{4} \times 36 $$
- Simplify the expression
Now, calculate the area:
$$ A = 9\sqrt{3} $$
This is the area of the equilateral triangle.
The area of the equilateral triangle is ( A = 9\sqrt{3} ).
More Information
The area of an equilateral triangle can be particularly useful in geometry and trigonometry. The formula uses the square of the side length, which shows the relationship between the size of the triangle and its area. Additionally, the factor of $\sqrt{3}$ arises from the geometric properties related to the angles and heights of the triangle.
Tips
- Forgetting to square the side length when using the formula.
- Not converting measurements into the same unit before calculating the area.
- Confusing the area formula of equilateral triangles with those of other types of triangles.
