Area of a Triangle can be calculated by various methods depending upon the available data of triangle. Different formulas used to calculate area of the triangle are explained here with examples.
The topic covers area of a triangle when
Method 1 Only base and height is given
Method 2 Two sides and included angle given
Method 3 All sides are given (Hero’s Formula)
Method 4 Area of an Equilateral Triangle
Calculate area of a triangle when only base and height is given.
Area of the Triangle with 
as base and 
as height
![\[Area = \frac{b.h}{2} \]](https://how-to-calculate.com/wp-content/ql-cache/quicklatex.com-0879f3b471039a908a5729ab15ef5567_l3.png "Rendered by QuickLaTeX.com")
Height should be perpendicular to base
Example: Find the area of a triangle with a base of 8 centimeters and a height of 5 centimetres
Area =(8.5)\2= 20 
Calculate area of a triangle when two sides and included angle are given
Suppose sides 
, and Angle ‘
‘ is given. The area is given by:
![\[Area = \frac{b.(a.sin A}{2} \]](https://how-to-calculate.com/wp-content/ql-cache/quicklatex.com-0315976569d10b1b19d1aa8a99b60daa_l3.png "Rendered by QuickLaTeX.com")
Calculate area of a triangle when all sides are given
Let ,,
be are the lengths of the sides of a triangle. The area is given by:
![\[Area=\sqrt{p.(p-a).(p-b).(p-c)} \]](https://how-to-calculate.com/wp-content/ql-cache/quicklatex.com-732b38c347efb54346bb00f4f90c2c3b_l3.png "Rendered by QuickLaTeX.com")
where, 
is the half of perimeter
![\[ p=\frac{(a+b+c)}{2}\]](https://how-to-calculate.com/wp-content/ql-cache/quicklatex.com-03b1fe55c3145433ab852cf9760c7db8_l3.png "Rendered by QuickLaTeX.com")
This is also called as Hero’s formula
Example:Find the area of a triangle with sides 5, 8 and 7 centimeters.
p=(5+8+7)/2=10
Calculate area of an equilateral triangle
An equilateral triangle have all sides equal and each angle 60°. therefore area of en equilateral triangle have different formula.
![\[Area = \frac{\sqrt{3}.a^2}{4} \]](https://how-to-calculate.com/wp-content/ql-cache/quicklatex.com-418e58a1e11af81eadebf7e7733c3878_l3.png "Rendered by QuickLaTeX.com")
where, is length of all side
Learn how to calculate area of trapezoid
Learn how to calculate area of Quadrilateral and other rectangular shapes
