How To Find Area of Triangle

What is Area of triangle?

The region enclosed by the boundary of the triangle i.e. area occupied by the perimeter of the triangle is termed the area of the Triangle.

How to Find Area of Triangle?

Area of the Triangle can be calculated using the following formulas,

1. For a Right Triangle: Area = (1/2) ⨯ base ⨯ height

2. Using Heron’s Formula: Area = √(s ⨯ (s – a) ⨯ (s – b) ⨯ (s – c)), where “s” is the semi-perimeter.

What is Area of Triangle with 3 sides?

If all the three sides of triangle are given, then its area is calculated using the Heron’s Formula.

Area = √{ s(s-a)(s-b)(s-c)}

where, a, b, and c are the sides of triangle and s is semi-perimeter = ​ ½ (a+b+c)

How To Find Area Of Triangle Without Height?

Without height, the area of triangle can be calculated using the Heron’s formula, which is :

Area of a triangle = √{s(s-a)(s-b)(s-c)}

where, a, b, and c are sides of the given triangle

and s = ½ (a+b+c) is the semiperimeter.

What is Area Of Equilateral Triangle?

Area of equilateral triangle is given by the following formula :

A = (√3)/4 × side². 

What is Area Of Isosceles Triangle?

Area of Isosceles Triangle is given by the following formula :

A = ¼ × b√(4a² – b²), where a= the two equal sides and b= the third side.

What is Area of Triangle in Coordinate Geometry?

When all three vertices of the triangle A(x₁, y₁), B(x₂, y₂) and C(x₃, y₃) are given then its area is calculated using the formula,

Area = 1/2 × [x₁(y₂ – y₃) + x₂(y₃ – y₁) + x₃(y₁ – y₂)]

What is Area of Triangle in Vector form?

If a triangle is formed by two vectors u, and v then its area is given by half of magnitude of product of the given vectors i.e.

Area = 1/2|[Tex]\vec{u}    [/Tex]×[Tex]\vec{v}    [/Tex]|

Area of a triangle is the region enclosed by all its three sides. It is generally calculated with the help of its base and height. To Find the Area of a triangle A with base b and height h, We use the formula, A = [Tex]\frac{1}{2} \times b \times h [/Tex].

Let’s learn about the area formulas for different types of triangles in detail, with the help of solved examples.