What is an Equilateral Triangle
An equilateral triangle is one whose sides have the same length and whose internal angles have the same measure. This is the fundamental property to be able to define a triangle as equilateral and what makes it part of regular polygons.
Equilateral triangle: sides and internal angles.
But equilateral triangles have other properties and characteristics further:
In addition to having three sides that measure exactly the same, the equilateral triangle has three internal angles that are also equal, that is, they are congruent.
Let us remember that the total sum of the internal angles of a triangle is 180º, so the measure of each internal angle in this case it is 60º.
Each of the external angles of an equilateral triangle measures 120º, which added to the measurement of the internal angle (60º) results in 180º. That is, the interior and exterior angles of an equilateral triangle are supplementary.
He center of symmetry of an equilateral triangle is the point where its medians meet. The medium They are the segments that join each of its vertices with the middle of the opposite side. In the equilateral triangle, the medians coincide with the height of the triangle.
Furthermore, all vertices of the equilateral triangle are located at the same distance from the center of the polygon. That is, if we draw a circle from said center, it will pass through each of the vertices of the triangle. The equilateral triangle, as with other regular polygons, is circumscribed to a circle.
Equilateral triangle formulas and examples
Perimeter
To calculate the perimeter of an equilateral triangle we must add all its sides, or what is the same, multiply the measurement of one of the sides by three.
By examplethe perimeter of the triangle in the image, whose sides measure 3 cm, will be 9 cm:
Height
The height is the segment that goes from the upper vertex to the middle of the base, dividing the triangle into two right triangles.
Since we only know the measurement of the sides of the triangle, and taking advantage of the resulting right-angled triangles, we are going to use the Pythagorean Theorem to calculate the value of the height.
The Pythagorean Theorem says that:
“In a right triangle, the hypotenuse squared is equal to the sum of the two legs squared.”
We know the value of towhich is 3 cm, and the value of c, which is 1.5 cm. We would need to know the value of h (height). Hence:
Therefore, now we know that the height of our triangle is 2.5 cm.
See also Pythagorean Theorem
Area
Now we can calculate the area of the equilateral triangle. To know the area of any triangle we must perform the calculation based on the following formula, where TO is the area, b is the base and h Is the height.
By examplewe are going to calculate the area of the triangle that we show in the image.
See also: