Equilateral Triangle Formula
Equilateral Triangle Formula
Equilateral triangles have equal sides, as the name suggests. Every Equilateral Triangle Formula has the same internal angles, namely 60 degrees.
According to the length of their sides, triangles can be divided into three types:
- The angles and sides of a scalene triangle are unequal.
- Triangles with equal sides and angles are called equilateral triangles.
- Two sides and two angles of an isosceles triangle are equal.
What is an Equilateral Triangle?
An equilateral triangle’s area is defined as the region enclosed by its three sides. Square units are used to express it. An equilateral triangle’s area is usually measured in square meters, cubic meters, and square yards. On the Extramarks educational portal, there is a discussion of the area of the Equilateral Triangle Formula, the altitude of the Equilateral Triangle Formula, the perimeter of the equilateral triangle, and the semi-perimeter of an equilateral triangle.
Area of Equilateral Triangle
Equilateral triangles occupy equal amounts of space in a two-dimensional plane. An equilateral triangle is a triangle with equal sides and 60° internal angles. The area of an equilateral triangle can be calculated if one of its sides is known. The educators at Extramarks can help students to clear basics about the concept easily and effectively.
Area of the Equilateral Triangle Formula
The equilateral triangle area formula is used to calculate the area between the sides of an Equilateral Triangle Formula in a plane.
Calculating the area of a triangle with a known base and height is as follows:
Half of the base times the height equals the area
An equilateral triangle’s area can be calculated using the following formula:
Area = √3/4 × (side)2 square units
Perimeter of the Equilateral Triangle Formula
Triangles have a perimeter equal to the sum of the lengths of their three sides, whether they are equal or not.
Three sides of an equilateral triangle make up its perimeter.
The formula P= 3a is used to calculate the perimeter of an Equilateral Triangle Formula, where ‘a’ represents one of the sides. In an equilateral triangle, all three sides are equal, so a + a + a = 3a.
The height is calculated as √3a/ 2
A semi perimeter is equal to (a + a + a)/2 = 3a/2
Formulas and Calculations for an Equilateral Triangle:
- P = 3a, the perimeter of an Equilateral Triangle Formula
- The formula for semi-perimeter of an Equilateral Triangle: s = 3a/2
- Area of Equilateral Triangle Formula: K = (1/4) * √3 * a2
- The angles of an Equilateral Triangle are A = B = C = 60 degrees
- The sides of an Equilateral Triangle Formula are a, b, and c.
- Find the perimeter, semi perimeter, area, and altitude of a triangle given its side.
- a is known here; find P, s, K, h.
- h = (1/2) * √3 * a
- P equals 3a
- s = 3a/2
- K = (1/4) * √3 * a2
- Find the side, semi-perimeter, area, and altitude of the triangle based on the perimeter.
- h = (1/2) * √3 * a
- a = P/3
- s = 3a/2
- K = (1/4) * √3 * a2
- Find the side, perimeter, area, and altitude of a triangle given its semi-perimeter.
- Semi perimeter (s) is known; find a, P, K, and h.
- h = (1/2) * √3 * a
- a = 2s/3
- P = 3a
- K = (1/4) * √3 * a2
- Calculate the area, side, perimeter, semi-perimeter, and altitude of the triangle given its area.
- K is known; find a, s, h and P.
- a = √
- P = 3a
- s = 3a / 2
- h = (1/2) * √3 * a
- (4/√3)∗K
- (4/√3)∗K equals 2 * √
- K/√3
- K/√3
- Find the side, perimeter, semi-perimeter, and area based on the altitude/height
- P = 3a
- s = 3a/2
- a = (2/√3) * h
- K = (1/4) * √3 * a2
Solved Example
- Find the area of an Equilateral Triangle Formula with 12 inches on each side using the equilateral triangle area formula.
Solution:
Side = 12 in
Using the equilateral triangle area formula,
Area = √3/4 × (Side)2
= √3/4 × (12)2
= 36√3 in2
Answer: Area of an Equilateral Triangle Formula is 36√3 in2
- Find the perimeter and semi-perimeter of an Equilateral Triangle Formula with 12 units of side measurement.
Solution:
The perimeter = 3a
Semi-perimeter = 3a/ 2
Given, side a = 12 units
Equilateral triangles have the following perimeter:
3 × 12 = 36 units
An equilateral triangle’s semi-perimeter is equal to:
36/2 = 18 units.
- Imagine an Equilateral Triangle Formula with a side of 5 cm. In the given equilateral triangle, what will be its perimeter?
The perimeter of an Equilateral Triangle Formula can be calculated using the formula 3a.
Here, a = 5 cm
Therefore, the perimeter equals 3 × 5 cm, or 15 cm.
FAQs (Frequently Asked Questions)
1. What is Napoleon's Theorem?
According to Napoleon’s theorem, equilateral triangles form on the sides of any triangle, whether they face outward or inward. This technique results in the inner or outer Napoleon triangle. The area difference between the outer and inner Napoleon triangles equals the size of the original triangle.
2. Does the Pythagorean theorem apply to equilateral triangles?
An Equilateral Triangle Formula has three equal sides and 60-degree angles. By drawing a perpendicular bisector line through the vertex of an equilateral, two right triangles are formed. Use the Pythagorean theorem and the height of right triangles within an equilateral triangle to determine the missing side lengths. The area of an equilateral triangle can hence be calculated using the formula A = √3/4 (a²). It is much easier to learn other trigonometric formulas if one knows how to calculate the height and area of a triangle with equal sides.
3. Do equilateral triangles have the possibility of being obtuse?
As an Equilateral Triangle Formula has equal sides and angles, each angle is sharp and measures 60 degrees, so it cannot be obtuse. Therefore, an equilateral angle cannot be obtuse. It is impossible for a triangle to be both right-angled and obtuse-angled at the same time. Due to the fact that a right-angled triangle only has one right angle, the other two angles are acute.
To In summary, an obtuse-angled triangle cannot form a right angle and vice versa. In a triangle, the longest side is opposite the obtuse angle.
4. Equilateral triangles are always congruent. Please explain.
Consider two triangles ABC and DEF with equal sides AB and DE.
AB=DE
Due to their equilateral nature, the other two pairs of sides are also equal.BC=EF
AC=DF
∴△ABC≅△DEF by SSS congruence criteria.
Therefore, two equilateral triangles with equal sides are always congruent.
5. What do all equilateral triangles have in common?
An Equilateral triangles have three congruent sides. The interior angles of the triangle are also equal. Equilateral triangles always have 60° angles.
6. What makes an equilateral triangle special?
In Equilateral triangles are triangles with equal-length sides. Due to the equal sides, the three opposite angles are equal in measurement as well. Due to its 60-degree angles, it is also called an equiangular triangle.
7. What are the different types of triangles?
Due to its equal angles and sides, an equilateral triangle is considered a regular polygon or triangle. Based on their sides, triangles can be classified into three types. These are isosceles, scalene, and equilateral.
8. Is it possible to have an equilateral shape for any shape?
A regular polygon and an edge-transitive polygon are both equilateral. Regular equilateral polygons are non-crossing and cyclic (the vertices are on circles). A convex equilateral quadrilateral is a rhombus (or perhaps a square).
