Triangle Formula

Triangle Formula

In geometry, a triangle is a polygon with three edges, and 3 sides, and three vertices. The most important property of triangles is that the sum of their interior angles equals 180 degrees, and this property is called the angle sum property of a triangle. Students can visit the Extramarks website and see the Triangle Formula.

If ABC is a triangle, it is represented as ΔABC where A, B, and C are the vertices of the triangle. A triangle is a two-dimensional shape in Euclidean geometry, displayed as three non-collinear points in a plane of eigenvalues. In the triangle,Perimeter = The sum of the 3 sides

The triangle is the whole location, which is enclosed by the 3 faces. Therefore, students need to recognise the bottom and top of it to locate the sector of a tri-sided polygon. Let us discover the locations of various forms of triangles.

What is the Triangle Formula?

The theorem says that the exterior angle of a triangle will always equal the sum of its opposite interior angles. For any two-dimensional (2D) shape, there are always two basic measurements you need to know. Therefore, a triangle has two basic formulas that help determine its area and perimeter. Let’s elaborate on the formula.

The perimeter of a Triangle Formula is the sum of all three sides of the triangle.

Perimeter of Triangle Formula = a + b + c

What is a Triangle?

A triangle is a closed shape with three corners, three sides, and three corners. A triangle with vertices P, Q and R is denoted by △PQR. The most common examples of triangles are triangle-shaped signs and sandwiches. Read more about triangles and triangle properties on Extramarks. A triangle is a simple polygon with three sides and three interior angles. It is one of the basic forms of geometry in which three vertices are connected, and is represented by the symbol △. There are different types of triangles, classified based on their sides and angles.

A triangle is made up of different parts. It has 3 corners, 3 sides, and 3 corners. Consider a triangle PQR that shows the triangle’s sides, vertices, and interior angles.

Perimeter of Triangle Formula

All geometric shapes have various features related to sides and angles that help identify them.

Here are some important properties of triangles:

A triangle has three sides, three angles, and three interior angles. The Sum of Angles property of a triangle indicates that the sum of the three interior angles of a triangle is always 180°. Consider the triangle PQR above, where angle P + angle Q + angle R = 180°. The triangle inequality theorem states that the sum of the lengths of the two sides of a triangle is greater than the length of the third side. According to the Pythagorean theorem, in a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides. i.e. (hypotenuse² = base² + height²). The side opposite the larger corner is the longest.

Area of a Triangle

The area of ​​a triangle is the space covered by the triangle, because it is two-dimensional, it is always measured in square units. Consider the triangle ABC below, which indicates the triangle base and elevation used to calculate the area of ​​theTriangle Formula .

area of Triangle Formula ​​

Area of ​​ΔABC = 1/2 x BC x AD where BC will be the base and AD will be the height of the triangle.

  •  Important note about triangles

A triangle is a shape with three closed sides, and there are two important formulas related to triangles. Heron’s formula and the Pythagorean theorem. The sum of the interior angles of a triangle is 180°, written as ∠1 + ∠2 + ∠3 = 180°.

Solved Example

The Isosceles Triangle’s AreaIn a triangle of isosceles angles,  facets are identical in duration. Also identical to every different are the 2 angles, contrary to the 2 identical facets.In case base and top are given, students use the subsequent formula:A = ½ × top × baseIf 3 facets are given :A = ½[√(a2 − b2/4) × b]Using 2 faces of the triangle and an perspective among them : A = ½ × b × c × sin(α)Using  angles among  facets and their duration :A = [c2 × sin(β) × sin(α)/ 2 × sin(2π−α−β)]

Area of Scalene Triangle Formula: A scalene triangle is a form of triangle wherein there are distinct facet dimensions on all 3 facets. The 3 angles are consequently distinct from each other because of this. A = ½ × top × base

Area of Equilateral Triangle Formula: There are all 3 facets of an equilateral triangle identical to every different. Therefore, all indoor angles are identical.

Each angle is 60°. A = (√three)/4 × side2, wherein A is the location of ​​the triangle. a is the duration of the triangle. b is the bottom of the triangle. c is his 0.33 facet of the triangle. h is the peak of the triangle. α and β are the angles among the 2 facets. A triangle is a triangular polygon. That is, locate the fringe of a triangle, which is, the sum of its facets. To locate the location of ​​a triangle, students first want to recognise the lengths of the edges of the triangle.

Conclusion

In geometry, a triangle is defined as a two-dimensional shape with 3 sides, 3 interior angles, and 3 vertices. A simple polygon with three vertices, represented by the triangle symbol, and triangles can be classified based on their sides and angles. Use the table below to understand the classification of triangles. This table shows the difference between six different types of triangles based on angles and sides. Triangle Classification Based on Sides and Angles .

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FAQs (Frequently Asked Questions)

1. What are the Triangle Formula?

The Triangle Formula is the area of ​​a triangle and the perimeter of a triangle. This Triangle Formula can be expressed mathematically as follows:

Area of ​​triangle, A = [(½) b × h]; where ‘b’ is the base of the triangle and ‘h’ is the height of the triangle. Perimeter of triangle, P = (a + b + c); where ‘a’, ‘b’, ‘c’ are the three sides of the triangle.

2. How many types of triangles are there in mathematics?

There are six types of triangles classified based on their sides and angles, as shown below.

  •  scalene triangle
  • isosceles triangle
  • equilateral triangle
  • acute triangle
  • obtuse triangle
  • right triangle

3. What is the area of ​​a concave-convex triangle?

The area of an odd triangle is equal to half the base times the height of the triangle. Therefore, the area of ​​a scalene triangle with base ‘b’ and height ‘h’ is expressed as “scalene triangle area.”

= 1/2 × b × h.