Equilateral Triangle
An equilateral triangle is a special type of triangle where all three sides are equal in length and all three angles are equal to 60 degrees
An equilateral triangle is a special type of triangle where all three sides are equal in length and all three angles are equal to 60 degrees. It is considered to be a regular polygon since it has equal sides and angles.
Properties of an equilateral triangle:
1. All three sides are equal: The lengths of all three sides of an equilateral triangle are equal. If we denote the length of one side as “s”, then the lengths of the other two sides are also “s”.
2. All three angles are equal: Each angle in an equilateral triangle is equal to 60 degrees. This means that the sum of all three angles is 180 degrees.
3. The height or altitude divides the triangle into two congruent right triangles: The height or altitude of an equilateral triangle is a segment drawn from one vertex perpendicular to the opposite side. It divides the triangle into two congruent right triangles, where the hypotenuse of each right triangle is a side of the equilateral triangle.
4. The height bisects the base: The height of an equilateral triangle also bisects the base, dividing it into two equal parts. Therefore, the height is also the perpendicular bisector of the base.
5. The center of a circumscribed circle coincides with the center of the triangle: The circumcircle of an equilateral triangle passes through all three vertices. The center of this circle coincides with the center of the equilateral triangle. The radius of the circumcircle is equal to the length of the sides of the triangle.
6. The area of an equilateral triangle: The area of an equilateral triangle can be calculated using the formula A = (s^2 * √3) / 4, where “s” is the length of a side. This formula can be derived by dividing the triangle into two congruent right triangles and calculating the area of one of these triangles.
Example:
Let’s say we have an equilateral triangle with a side length of 8 units. To find its area, we use the formula: A = (s^2 * √3) / 4.
Plugging in the given values, we get:
A = (8^2 * √3) / 4
A = (64 * √3) / 4
A = 16√3 square units.
Therefore, the area of the equilateral triangle with a side length of 8 units is equal to 16√3 square units.
More Answers:
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