Finding the Side Length of an Equilateral Triangle with an Area of 1.5 cm2

Finding the Side Length of an Equilateral Triangle with an Area of 1.5 cm2

Haven't tackled one of these in a while! Upon revisiting this problem, we often find ourselves needing to determine the side length of an equilateral triangle given its area. In this context, we are dealing with a 1.5 cm2 equilateral triangle, and in this article, we'll explore how to find the side length step-by-step.

Understanding the Basics

Equilateral triangles are a special type of triangle where all three sides and all three internal angles are equal. Each angle in an equilateral triangle measures 60°.

The area of any triangle can be calculated using the formula:

Area 1/2 x base x height

However, given the complexity of an equilateral triangle, direct application of the base-height formula can be tricky. Instead, trigonometric relationships come in handy.

Using Trigonometry

In an equilateral triangle, the altitude (height) divides the base into two equal halves. If we let the side length of the equilateral triangle be s, then the base is s, and the height is the altitude, which can be expressed using trigonometry:

Height (h) s * sin(60°) s * √3 / 2

Substituting the height into the area formula, we have:

1.5 1/2 * s * (s * √3 / 2)

Let's simplify this equation step-by-step:

Step-by-Step Solution

Simplify the equation inside the parentheses:

1.5 1/2 * s2 * √3 / 2

Multiply the numerator on the right-hand side:

1.5 (s2 * √3) / 4

Clear the fraction by multiplying both sides by 4:

6 s2 * √3

Solve for s2 by dividing both sides by √3:

s2 6 / √3

Simplify the right-hand side:

s2 2 * √3

Take the square root of both sides to solve for s:

s √(2 * √3)

Equivalent to:

s ≈ 1.633 cm

Conclusion

Through the use of trigonometric relationships and algebraic manipulation, we have determined that the side length of an equilateral triangle with an area of 1.5 cm2 is approximately 1.633 cm. This process highlights the usefulness of understanding geometric principles and trigonometry in solving complex problems.

Related Keywords

equilateral triangle area side length

Explore Further

If you're interested in more geometric concepts and problem-solving techniques, consider exploring topics such as:

The area and properties of equilateral triangles Using trigonometry to solve geometric problems Basic algebra and its applications in geometry

By delving into these areas, you can enhance your mathematical skills and deepen your understanding of geometric principles.