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

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

Side a
Side b
Angle α° between parties a and b

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

3

Side a
Side b
Side c

4

## 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

Semi-perimeter:

Side a
Side b
Side c

6

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

Side a
Angle β°
Angle α°

For isosceles triangles

7

Side a (a = b)
Side c

8

## 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

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

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 base of the triangle c
Height h

12

## Area of an equilateral triangle on the side

Side a (a = b = c)

13

Height h

14

15

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

Radius R of the circumscribed circle

For right-angled triangles

16

Cathete a
Cathete b

17

Side c
Angle α

18

Side b
Angle α

19

Line segment d
Line segment e

20

Side с

21

## 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.