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Oct 9, 2024 · h = a × √3 / 2. Substituting h into the first area formula, we obtain the equation for the equilateral triangle area: area = a² × √3 / 4. 2. Using trigonometry. Let's start with the trigonometric triangle area formula: area = (1/2) × a × b × sin(γ), where γ is the angle between the sides. We remember that all sides and all angles ...
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In geometry, an equilateral triangle is a triangle that has all its sides equal in length. Since the three sides are equal therefore the three angles, opposite to the equal sides, are equal in measure. Therefore, it is also called an equiangular triangle, where each angle measure 60 degrees. Just like other types of triangles, an equilateral ...
- 6 min
- A triangle that has all its sides equal in dimension and each angle measure up to 60 degrees, is called an equilateral triangle.
- The formula to find area of equilateral triangle is given by: A = (√3/4)a2, where a is the length of side of equilateral triangle.
- The perimeter of an equilateral triangle is the sum of all its three equal sides. Perimeter = 3a, where a is the length of its sides.
- The formula to find the height of equilateral triangle is: Height, h = (√3/2)a, where a is the side of the equilateral triangle.
- An equilateral triangle is a regular polygon or a regular triangle.
- Based on sides, there are three different kinds of triangles. Their names are: Scalene triangle Isosceles triangle Equilateral triangle
- All triangles have 3 sides only.
- Perimeter = 3 x sides of equilateral triangle Perimeter = 3 x 10 = 30 cms
Equilateral Triangle Examples. Example 1: Calculate the area of an equilateral triangle whose sides are 20 inches. Solution: Area of equilateral triangle = √3a 2 / 4, where a is the side. Given, a = 20 inches. Therefore, area = √3×20×20 / 4. Area of an equilateral triangle = 100√3 square inches.
- Definition of Equilateral Triangle
- History of Equilateral Triangles
- Equilateral Triangles Used in Real Life
- What Are Not Equilateral Triangles?
- Properties of Equilateral Triangles
- Perimeter and Area of Equilateral Triangle
- Fun Facts About An Equilateral Triangle
- Solved Examples
In geometry, an equilateral triangle is a triangle whose all three sides are of equal length. The sides of an equilateral triangle are congruent, which means that all sides are of equal length. All the interior angles are equal(60 degrees) too. The term equilateral is made up of ‘equi,’ which means equal, and ‘lateral,’ which means side. So, a tria...
The traces of triangles can be found all over the world, especially in construction. The ancient Egyptians were fond of them. The faces of the famous Pyramids of Egypt are triangular. The pyramids of Giza are the most famous pyramids built by the Egyptians in the second century B.C. Egyptians thought that the triangular shape of the pyramid symboli...
The traffic sign boards we see on the road are in the shape of equilateral triangles. Next time you go out for a car ride, notice that all the three sides of a signboard seem to be of equal length.
The face of a traffic cone is not an equilateral triangle because all three sides are not equal. A traffic cone has elongated sides with a smaller base.Sails on a sailing boat are not equilateral triangles since the sides are not equal in length. Two of the sides are longer than the remaining side.All sides are of the same length ‘a’All interior angles are equal to 60 degrees.An equilateral triangle is symmetrical, which means if you fold it to join its vertices, it will fold with the two halves perfectly overlapping each other.You can calculate the perimeter(length of the whole boundary) of an equilateral triangle by adding the lengths of all three sides. In an equilateral triangle of side length ‘a’, the lengths of the...The area of an equilateral triangle can be calculated using the formula, Area = 34)×a2; where a is the side of an equilateral triangle.The faces of the Pyramids of Giza in Egypt are one of the world’s oldest and largest examples of equilateral triangles. They were built in the 26th century B.C. and are perfectly equilateral.An equilateral triangle is a special isosceles triangle having all the three sides equal.Q1. What will be the perimeter of an equilateral triangle, assuming that all its sides are 30 inches in length? Solution: You know that the perimeter of an equilateral triangle is 3 times the side length. It is given in the question that side length = 30 inches. Therefore, the perimeter of an equilateral triangle will be 3 × 30 = 90 inches. Q2. Wha...
An equilateral triangle, in geometry, is a triangle with three equal sides. Also the interior angles of an equilateral triangle are equal. As a result, each angle measures 60 degrees. Hence, it is sometimes referred to as an equiangular triangle. Equilateral triangles follow the same area, perimeter, and height formula as other types of triangles.
The equilateral triangle is also the only triangle that can have both rational side lengths and angles (when measured in degrees). When inscribed in a unit square, the maximal possible area of an equilateral triangle is \(2\sqrt{3}-3\), occurring when the triangle is oriented at a \(15^{\circ}\) angle and has sides of length \(\sqrt{6}-\sqrt{2}:\)
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An equilateral triangle is also called an equiangular triangle since its three angles are equal to 60°. In an isosceles triangle, the base angles are congruent. Recall from above that an equilateral triangle is also an isosceles triangle. Since DE≅EF, the base angles, ∠D and ∠F, are congruent. Also, since DE≅DF, ∠E≅∠F, so by the ...
