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# Triangle calculator -height, area, perimeter, sides

Triangle calculator will help you calculate the area, perimeter, sides, height, angles of any triangle, right triangle and equilateral.   Okrąg opisany Okrąg wpisany

a, b, c - side lengths;
ha, hb, hc - heights from sides a, b, c;
α, β, γ - angles opposite the sides a, b, c;
S - area;
R - radius of the circumscribed circle;
r - radius of the inscribed circle;
p - half the perimeter of the triangle;

## Triangle - Area from sides and height

$$\Large{S=\frac{ah_a}{2}= \frac{bh_b}{2}=\frac{ch_c}{2} }$$
Side length a, b or c

Height to the side ha, hb or hc

Area (S)

## Triangle - Area from sides and angle

$$\Large{S=\frac{ab\sin\gamma}{2}= \frac{bc\sin\alpha}{2}=\frac{ca\sin\beta}{2} }$$

Side length a or b

Side length b or c

Angle according to the sides α, β or γ =

Area (S)

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## Triangle - Area from Heron formula

$$\Large{S=\sqrt{p(p-a)(p-b)(p-c)} }$$

Length side (a)

Length side (b)

Length side (c)

Area (S)

## Equilateral triangle - Area

$$\Large{S=\frac{a^2\sqrt{3}}{4}\approx 0.433a^2 }$$

Length side (a)

Area (S)

## Isosceles triangle - Area

$$\Large{S=a^2\frac{\cos\beta +1}{4\sin\beta}= \frac{b^2\sin\beta}{2} }$$

Angle (β) opposite to the base (a)

Length side (a)
or
Length side (b)

Area (S)

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## Triangle - Perimeter

$$\Large{P=a+b+c }$$

Length side (a)

Length side (b)

Length side (c)

Perimeter (P)

Half the perimeter
$$\Large{P=\frac{a+b+c}{2} }$$

## Triangle - Center of gravity (center of mass , barycenter)

$$\Large{Q=\Biggl(\frac{a_1+b_1+c_1}{3}, \frac{a_2+b_2+c_2}{3}\Biggr)}$$
Coordinates of the triangle's vertices in the Cartesian system

A=(a1, a2)
a1
a2

B=(b1, b2)
b1
b2

C=(c1, c2)
c1
c2