Key Concepts and Properties of Equilateral Triangles: Side Length, Perimeter, Area, Height, and Interior Angles

equilateral triangle

An equilateral triangle is a special type of triangle where all three sides are equal in length

An equilateral triangle is a special type of triangle where all three sides are equal in length. In addition, all three angles in an equilateral triangle are also equal, measuring 60 degrees each.

To better understand the properties of an equilateral triangle, let’s discuss some key concepts related to it:

1. Side length: In an equilateral triangle, all three sides are of the same length. Let’s call this length ‘s’. So, each side of an equilateral triangle is ‘s’ units long.

2. Perimeter: The perimeter of any polygon is the sum of all its side lengths. For an equilateral triangle, the perimeter can be calculated by adding the lengths of all three sides. Therefore, the perimeter of an equilateral triangle is 3s.

3. Area: The area of an equilateral triangle can be calculated using multiple methods, but one common approach is to use the formula:

Area = (sqrt(3)/4) * s^2

Here, ‘s’ is the side length of the equilateral triangle. The formula derives from dividing the equilateral triangle into two congruent right-angled triangles and finding their combined area.

4. Height: The height of an equilateral triangle is a perpendicular line segment drawn from one vertex of the triangle to the midpoint of the opposite side. In an equilateral triangle, the height will also be the line of symmetry.

5. Interior angles: As mentioned earlier, all three angles of an equilateral triangle are equal and measure 60 degrees each. The sum of the interior angles of any triangle is always 180 degrees, so in an equilateral triangle, the measure of each angle is 60 degrees (180/3).

Remember these key properties when working with equilateral triangles or solving related problems.

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