Calculate the area of the triangle.
Understand the Problem
The question is asking to calculate the area of an equilateral triangle with a side length of 4 cm. The area can be calculated using the formula for the area of an equilateral triangle: Area = (sqrt(3)/4) * side^2.
Answer
The area of the triangle is approximately $6.93 \, \text{cm}^2$.
Answer for screen readers
The area of the equilateral triangle is approximately $6.93 , \text{cm}^2$.
Steps to Solve
- Identify the formula for area of an equilateral triangle
To calculate the area of an equilateral triangle, we use the formula:
$$ \text{Area} = \frac{\sqrt{3}}{4} \times \text{side}^2 $$
- Substitute the side length into the formula
Given that the side length of the triangle is 4 cm, substitute this value into the formula:
$$ \text{Area} = \frac{\sqrt{3}}{4} \times (4)^2 $$
- Calculate the square of the side length
First, calculate ( (4)^2 ):
$$ (4)^2 = 16 $$
- Insert the squared value into the area formula
Substituting the squared value back into the area formula gives:
$$ \text{Area} = \frac{\sqrt{3}}{4} \times 16 $$
- Simplify the equation
Now, divide 16 by 4:
$$ \text{Area} = \sqrt{3} \times 4 $$
- Calculate the area
Finally, compute the numerical value:
$$ \text{Area} \approx 4 \times 1.732 \approx 6.928 \text{ cm}^2 $$
The area of the equilateral triangle is approximately $6.93 , \text{cm}^2$.
More Information
The area of an equilateral triangle is always calculated using the formula that involves the square of the side length. The approximation of $\sqrt{3}$ is about 1.732, which is used for calculations.
Tips
- Forgetting to square the side length before substituting it into the area formula.
- Incorrectly calculating the value of $\sqrt{3}$.
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