Thursday , October 18 2018
Calculators

How to calculate area of a Triangle

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 a triangle

 

Area of the Triangle with b as base and h as height

    \[Area  = \frac{b.h}{2} \]

Height h should be perpendicular to base b

Example: Find the area of a triangle with a base of 8 centimeters and a height of 5 centimetres

Area =(8.5)\2= 20 cm^2

 

Calculate area of a triangle when two sides and included angle are given

Suppose sides a,b and Angle ‘A‘ is given. The area is given by:

    \[Area  = \frac{b.(a.sin A}{2} \]

Calculate area of a triangle when all sides are given

Let a,b,c be are the lengths of the sides of a triangle. The area is given by:

    \[Area=\sqrt{p.(p-a).(p-b).(p-c)} \]

where, p is the half of perimeter

    \[ p=\frac{(a+b+c)}{2}\]

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

Area=\sqrt{(10.(10-5).(10-8).(10-7))}  =17.32 cm^2

 

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.

    \[Area  = \frac{\sqrt{3}.a^2}{4} \]

where, a is length of all side

 

Learn how to calculate area of trapezoid

Learn how to calculate area of Quadrilateral and other rectangular shapes

Authored by howtocalculate

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