Triangle Formula

Triangle Formula

Triangles are polygons that have three sides and three vertices. It is one of the most fundamental concepts in geometry. A triangle containing vertices A, B, and C is denoted as △ ABC. In Euclidean geometry, any three non-collinear points define both a unique triangle and a unique plane simultaneously. A triangle contains three angles. Each angle is generated when any two sides of a triangle intersect at a common point, known as the vertex.

Triangle formulae are the fundamental formulas used to calculate the unknown dimensions and characteristics of a triangle. The main formulae for a triangle are linked to its area and perimeter. Let us understand more about each triangle formula in detail.

What is the Triangle Formula?

The two most essential triangle formulae are for the area and perimeter of a triangle. There are several triangle formulae that apply to various sorts of triangles. Let us study all of the basic triangle फॉर्मूले। Triangle formulae primarily contain formulas for calculating a triangle’s area and perimeter. Let’s learn more about them in the next sections.

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

The perimeter of any polygon is the sum of the lengths of the edges.

In the triangle,

Perimeter = The sum of the three sides

Here are some important properties of triangles:

• The perimeter of a triangle is equal to the sum of all the sides of the triangle, and the formula is expressed as, Perimeter of a triangle formula, P = (a + b + c), where ‘a’, ‘b’, and ‘c’ are the three sides of the triangle.
• The equilateral triangle formula for perimeter is, Perimeter of equilateral triangle = (a +a + a) = 3a. Here ‘a’ is a side of an equilateral triangle. (Note: In an equilateral triangle, all three sides are equal)
• The isosceles triangle formula for perimeter is Perimeter of isosceles triangle = (s + s + b) = (2s + b). Here ‘s’ is the length of the two equal sides, and ‘b’ is the base of an isosceles triangle.

Area of a Triangle

The triangle’s area is the total region that is enclosed by the three sides of any particular triangle. It is equal to half of the height of the basic periods. Therefore, we have to know the base and height of it to find the field of a tri-sided polygon.

Let us find out the area of different types of triangles.

 Important note about triangles

• The area of a triangle is equal to half the product of the base and height of the triangle and it is expressed as, Area of triangle = ½ × base × height
• While the above formula is used for any triangle, sometimes, in the case of a scalene triangle, we use the Heron’s formula to find its area.
• The area of a triangle using Heron’s Formula is given as, Area of scalene triangle = $\sqrt{s(s-a)(s-b)(s-c)}$
• , where ‘s’ is the semi-perimeter of the triangle. So, semi-perimeter = Perimeter/2 = (a + b + c)/2
• In case of an equilateral triangle, the area can be calculated using the formula, Area of equilateral triangle = (√3/4)a², where ‘a’ is the side of the triangle.
• In the case of an isosceles triangle, the isosceles triangle formula for area is, Area of isosceles triangle = 1/2 × Base × Height, where, height = $\sqrt{{\text{a}}^2-\frac{b^2}{4}}$
• . (Here ‘a’ is the equal side, and ‘b’ is the base of the isosceles triangle.)
• The Pythagoras theorem can be used to find the unknown side of a right-angled triangle if the other two sides are known. This theorem is mathematically expressed as, h² = p² + b². Here, ‘h’ is the hypotenuse (longest side of a right triangle), ‘p’ is the perpendicular side, and ‘b’ is the Base. Once all the sides are known, the area of the triangle can be calculated using the formulas given above.

Solved Examples on Triangle Formulas

Example 1: Calculate the area of a triangle whose base is 80 units and whose height is 50 units.

Solution:

To find: The area of a triangle

The base of a triangle = 80 units (given)

Height of triangle = 50 units (given)

Using triangle formulas,

Area of triangle, A = ½ × base × height

= ½ × 80 × 50

= 2000 square units

Answer: The area of the triangle is 2000 square units.

Example 2: A triangle has sides a = 10 units, b = 20 units, and c = 30 units. What is the perimeter of this triangle?

Solution:

To find: The perimeter of a triangle

Three sides of a triangle = 10, 20, 30. (Given)

Using triangle formulas,

Perimeter of a triangle, p = (a + b + c)

= 10 + 20 + 30

= 60 units

Answer: The perimeter of the given triangle is 60 units.