geometry

What is an Equilateral Triangle?

There are many types of triangles in geometry. Have you heard of equilateral triangles?

Let’s learn more about equilateral triangles. As the name suggests, an equilateral triangle is one in which all 3 sides of the triangle are the same length. Assume a triangle named PQR, and the sides are PQ = QR = RP.

Furthermore, an equilateral triangle, like every triangle, has three angles, all of which are congruent and all of which are equivalent to 60 degrees. The sum of the three angles of any given equilateral triangle equals 180 degrees. 180° is equivalent to 60° + 60° + 60°. As a result, any given equilateral triangle obeys the triangle’s angle sum property.

In this article, we are going to discuss more equilateral triangles and the area of equilateral triangles.

How do you find the Area of the Equilateral Triangle?

The formula of an equilateral triangle area is used to compute the space in a plane occupied by the sides of an equilateral triangle. Many people utilize the ability to calculate the areas of any surface in their work. We already know the formula to calculate the area of an equilateral triangle. Calculating the area of any given triangle in a general triangle can be a little tricky in some instances. However, calculating the area of any given equilateral triangle is a simple computation.

The general formula for calculating the area of a triangle with known base and height is as follows:

Area = ½ * height * base

The area of an equilateral triangle can be calculated using the following formula:

The area of an equilateral triangle is equal to a*a square units, where a = the length of each side of an equilateral triangle.

Properties of Equilateral Triangle

  • Each of an equilateral triangle’s three sides is equal.
  • Each of an equilateral triangle’s three angles is congruent and equals 60 degrees.
  • An equilateral triangle is defined as a regular polygon with 3 sides.
  • The perpendicular drawn from the vertex of the equilateral triangle to the opposite side split it into equal halves. In addition, the angle created by the vertex wherein the perpendicular of the triangle is drawn is divided into two equal 30-degree angles.
  • An equilateral triangle’s ortho-center and centroid are both situated at the same point.
  • In any given equilateral triangle, all three sides of the triangle have the same median, angle bisector, & height.
  • 3*a is the formula to calculate the perimeter of an equilateral triangle, where an is a side of the triangle.

Examples

  1. You have been given an equilateral triangle ABC, one side of the equilateral triangle AB = 5 cm. What will be the measure of the rest of the sides of the triangle?

Solution: In any given triangle ABC, since ABC is an equilateral triangle all the sides of the equilateral triangle have the same measure, AB = 5 cm

Therefore, the rest of the two sides have the same measure too. Sides BC = 5 cm & CA = 5 cm.

  1. You have been given an equilateral triangle PQR, one side of the equilateral triangle PQ = 6 cm. What will be the measure of the rest of the sides of the triangle?

Solution: In any given triangle PQR, since PQR is an equilateral triangle all the sides of the equilateral triangle have the same measure. PQ = 6 cm

Therefore, the rest of the two sides have the same measure too. Sides QR = 6 cm & RP = 6 cm

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