Mastering the Geometry of Equilateral Triangles: Perimeter, Area, Height, and Angles

Equilateral Triangle

An equilateral triangle is a triangle that has three sides of equal length and three angles of equal measure

An equilateral triangle is a triangle that has three sides of equal length and three angles of equal measure. It is a special type of triangle because all sides and angles are congruent.

In an equilateral triangle, all three sides are equal in length. Let’s call this length “s”. The perimeter of an equilateral triangle is given by the formula P = 3s, where P represents the perimeter.

To calculate the area of an equilateral triangle, we can use the formula A = (s^2 * √3) / 4, where A represents the area. The √3 here is the square root of 3.

The formula for finding the height of an equilateral triangle can be derived from the Pythagorean theorem. If we draw a line from one vertex to the midpoint of the opposite side, this line is considered the height. The height of an equilateral triangle, h, can be calculated using the formula h = (s * √3) / 2.

Since all three angles in an equilateral triangle are congruent, each angle measures 60 degrees. This is because the sum of the angles in any triangle is always 180 degrees.

In summary:
– All sides of an equilateral triangle are equal in length.
– The perimeter of an equilateral triangle is P = 3s, where s is the length of one side.
– The area of an equilateral triangle is A = (s^2 * √3) / 4.
– The height of an equilateral triangle is h = (s * √3) / 2.
– Each angle in an equilateral triangle measures 60 degrees.

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