Area of a triangle

Area of triangle, formulas and calculator for calculating area in online mode. General formulas for all types of triangles, special cases for equilateral, isosceles and rectangular triangles are given.


For all triangles



1

The area of the triangle by its base and height

The area of the triangle by its base and height

The area of the triangle is equal to half the product of the base of the triangle by the height dropped on this base: . The triangle's base can be chosen from either side of the triangle.

Calculate area:

Side a
Height h




2

The area of the triangle on two sides and the angle between them

The area of the triangle on two sides and the angle between them

The area of the triangle is equal to half the product of any two of its sides by the sine of the angle between these sides: . The angle α between the sides can be anything: blunt, sharp, straight.

Calculate area:

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




3

The area of the triangle along the radius of the inscribed circle and the three sides

The area of the triangle along the radius of the inscribed circle and the three sides

The area of the triangle is equal to half the sum of all three sides of the triangle multiplied by the radius of the inscribed circle.


or in another way you can say: The area of the triangle is equal to half the perimeter of the triangle multiplied by the radius of the inscribed circle.

Calculate area:

Side a
Side b
Side c
Radius r inscribed circle




4

The area of the triangle along the radius of the circumscribed circle and the three sides

The area of the triangle along the radius of the circumscribed circle and the three sides

The area of the triangle is equal to the product of three sides of the triangle divided by four radii of the circumscribed circle:

Calculate area:

Side a
Side b
Side c
Radius R of the circumscribed circle




5

The area of the triangle according to Heron's formula

The area of the triangle according to Heron's formula

If you know all three sides of a triangle, you can calculate its area using the Heron formula: , where p is the half -perimeter of the triangle, calculated by formula

Calculate area:

Side a
Side b
Side c
Semi-perimeter:




For isosceles triangles


6

The area of an isosceles triangle along the sides and the angle between them

The area of an isosceles triangle along the sides and the angle between them

Calculate area:

Side a (a = b)
Angle α° between the sides




7

The area of an isosceles triangle along the sides and the angle between them

The area of an isosceles triangle along the sides and the angle between them

Calculate area:

Side a (a = b)
The base of the triangle c
Angle β° between base and side




8

The area of an isosceles triangle on the base and angle between the sides

The area of an isosceles triangle on the base and angle between the sides

Calculate area:

The base of the triangle c
Angle α° between the sides




For equilateral triangles


9

The area of an equilateral triangle on the side

The area of an equilateral triangle on the side

Calculate area:

Side a (a = b = c)




10

The area of an equilateral triangle in height

The area of an equilateral triangle in height

Calculate area:

Height h




11

The area of an equilateral triangle along the radius of the inscribed circle

The area of an equilateral triangle along the radius of the inscribed circle

Calculate area:

Radius r inscribed circle




12

The area of an equilateral triangle along the radius of the circumscribed circle

The area of an equilateral triangle along the radius of the circumscribed circle

Calculate area:

Radius R of the circumscribed circle




For right-angled triangles


13

Square of a right triangle with two legs

Square of a right triangle with two legs

Calculate area:

Cathete a
Cathete b




14

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

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

Calculate area:

Line segmentd
Line segment e




15

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

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

Heron's formula for a right triangle , where p is the half -perimeter of the triangle, calculated by formula

Calculate area:

Side a
Side b
Side c

Semi-perimeter:





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