How to Find Area of a Triangle? – Formulae, Examples

The area of a triangle is an enclosed area over a two-dimensional plane. A triangle, as we know, is a closed form with three sides and three vertices. Hence, the area of a triangle is the total space occupied by its three sides. The area of a triangle is calculated by taking half the product of its base and height. 

In general, an “area” is defined as the region inhabited inside the boundaries of a flat object or figure. The measurement is done in square units (m2). There are standard formulas for calculating the area for squares, rectangles, circles, triangles, and so on. Let’s go through some areas of triangle formulae and examples of triangles. 

What is the Area of a Triangle?

The area of a triangle is the entire space occupied by its three sides in a two-dimensional plane. 

Area of Triangle Formula

The formula for the area of a triangle \(A= \frac{1}{2} bh\) 

This formula applies to all triangles. It is important to remember that the base and height of a triangle are perpendicular to one another. 

How to Find Area of a Triangle? - Formulae, Examples

What is the Perimeter of a Triangle?

The perimeter of any two-dimensional shape is defined as the distance around the shape. We can compute the perimeter of any closed object by summing the lengths of each of its sides. 

Perimeter = Sum of the three sides 

What is Heron’s Formula?

Heron’s formula is used to calculate the area of a triangle given the lengths of all its sides. 

Area of a Triangle with Three Sides

Heron’s formula may be used to calculate the area of a triangle with three sides of varying lengths. Heron’s formula has two critical phases. The first step is to calculate the semi-perimeter of a triangle by summing all three sides and dividing by two. The following step is to use the semi-perimeter of a triangle value in the primary formula known as “Heron’s Formula” to calculate the area of a triangle. 

\(Area = \sqrt{s(s-a)(s-b)(s-c)}\)

Area of Triangle for Right-Angled Triangle

A right-angled triangle is a right triangle that has one 90° angle. As a result, the triangle’s height matches the perpendicular side’s length. 

\(A= \frac{1}{2}*Base*Height\)

Area of Triangle for Equilateral Triangle

A triangle with 3 equal sides is called an equilateral triangle. The perpendicular traced from the triangle’s vertex to its base splits the base into two equal pieces. To calculate the area of an equilateral triangle, simply determine the lengths of its sides. 

Area of an Equilateral Triangle = \(A=\frac{ \sqrt{3} }{4} side^{2}\)

Area of Triangle for Isosceles Triangle

An isosceles triangle has two equal sides and equal angles opposing the equal sides. 

\(A= \frac{1}{4}b \sqrt{4 a^{2}- b^{2} }\)

Examples of Areas of Triangle

Unit 9 Section 5 : The Area of a Triangle

Final Notes

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What are the Formulae for the Area of the Triangle? 

\(A= \frac{1}{2} bh\)

What are the Types of Triangles? 

  • Scalene Triangle. 
  • Isosceles Triangle. 
  • Equilateral Triangle. 
  • Acute Angle Triangle. 
  • Right Angle Triangle. 
  • Obtuse Angle Triangle. 

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