Geometry

Area of a triangle

Area of a triangle, formulas for calculating the area of various types of triangles depending on the known source data, a calculator for finding the area online and a table with the area formulas of the triangles.


Table with triangle area formulas (at the end of the page)

Download triangle area formulas as a picture or file PDF (at the end of the page)



For all triangles



1

Area of triangle by its base and height

Area of triangle by its base and height
Side a
Height h

The triangle's base can be chosen from either side of the triangle.


2

Area of triangle on two sides and the angle between them

Area of triangle on two sides and the angle between them
Side a
Side b
Angle α° between parties a and b

The angle α between the sides can be anything: blunt, sharp, straight.


3

Area of triangle along the radius of the inscribed circle and the three sides

Area of triangle along the radius of the inscribed circle and the three sides
Side a
Side b
Side c
Radius r inscribed circle

4

Area of triangle along the radius of the circumscribed circle and the three sides

Area of triangle along the radius of the circumscribed circle and the three sides
Side a
Side b
Side c
Radius R of the circumscribed circle

5

Area of triangle according to Heron's formula

Area of triangle according to Heron's formula
Semi-perimeter: 

Side a
Side b
Side c

6

Area of an arbitrary triangle on the side and two adjacent corners

Area of an arbitrary triangle on the side and two adjacent corners
Side a
Angle β°
Angle α°


For isosceles triangles


7

The area of the isosceles triangle on the sides and base

The area of the isosceles triangle on the sides and base

Side a (a = b)
Side c

8

Area of an isosceles triangle along the sides and the angle between them

Area of an isosceles triangle along the sides and the angle between them
Side a (a = b)
Angle α° between the sides

9

Area of an isosceles triangle on the side, base and angle between them

Area of an isosceles triangle on the side, base and angle between them
Side a (a = b)
The base of the triangle c
Angle β° between base and side

10

Area of an isosceles triangle on the base and angle between the sides

Area of an isosceles triangle on the base and angle between the sides
The base of the triangle c
Angle α° between the sides


For equilateral triangles


11

The area of an isosceles triangle in height and base

The area of an isosceles triangle in height and base

The base of the triangle c
Height h


12

Area of an equilateral triangle on the side

Area of an equilateral triangle on the side
Side a (a = b = c)

13

Area of an equilateral triangle in height

Area of an equilateral triangle in height
Height h

14

Area of an equilateral triangle along the radius of the inscribed circle

Area of an equilateral triangle along the radius of the inscribed circle
Radius r inscribed circle

15

Area of an equilateral triangle along the radius of the circumscribed circle

Area of an equilateral triangle along the radius of the circumscribed circle
Radius R of the circumscribed circle


For right-angled triangles


16

Square of a right triangle with two legs

Square of a right triangle with two legs
Cathete a
Cathete b

17

Area of a right triangle through hypotenuse and angle

Area of a right triangle through hypotenuse and angle

Side c
Angle α

18

Area of a right-angled triangle through a leg and angle

Area of a right-angled triangle through a leg and angle

Side b
Angle α

19

Area of a right-angled triangle along the segments dividing the hypotenuse into an inscribed circle

Area of a right-angled triangle along the segments dividing the hypotenuse into an inscribed circle
Line segment d
Line segment e

20

Area of a right-angled triangle through the hypotenuse and inscribed circle

Area of a right-angled triangle through the hypotenuse and inscribed circle

Side с
Radius r

21

Area of a right-angled triangle according to Heron's formula

Area of a right-angled triangle according to Heron's formula
Semi-perimeter: 

Side a
Side b
Side c



Our calculator for calculating the area will help you calculate the area of different types of triangles or check the already performed calculations.

Various formulas are used to calculate the area of a triangle, depending on the known input data. Above are formulas and a calculator that will help calculate the area of a triangle or check already performed calculations. General formulas are given for all types of triangles, special cases for equilateral, isosceles and right triangles.


Depending on the type of triangle and its known source data, the area of the triangle can be calculated using various formulas.


Table with triangle area formulas


initial data
(active link to go to the calculator)
sketch formula
For all triangles
1 base and height
2 two sides and the angle between them
3 circle radius and three sides
4 radius of the circumscribed circle and three sides
5 three sides
(according to Heron’s formula)

Where 
6 side and two adjacent corners
For isosceles triangles
7 sides and base
8 sides and angle between them
9 sides, base and angle between sides and base
10 base and angle between the sides
11 height and base
For equilateral triangles
12 side
13 height
14 circle radius
15 radius of the circumscribed circle
For right-angled triangles
16 two legs
17 hypotenuse and angle
18 leg and corner
19 segments into which the inscribed circle divides the hypotenuse
20 hypotenuse and inscribed circle radius
21 three sides
(according to Heron’s formula)

Where  


Definitions


The area of a triangle is a numerical characteristic characterizing the size of a plane limited by a geometric figure formed by three segments (sides) that connect three points (vertices) that do not lie on one straight line.

A triangle is a geometric figure formed by three segments that connect three points that are not lying on one straight line. The segments are called the sides of the triangle, and the points are the vertices of the triangle.

Area - is a numerical characteristic characterizing the size of a plane bounded by a closed geometric figure.


Area is measured in units of measurement squared: km2, m2, cm2, mm2, etc.


Download triangle area formulas as a picture



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