Triangle
In a plane, a polygon with three sides.
For measurement purposes, we establish a base b, and a height h relative to the base.
Properties
- A planar triangle is a convex figure.
- The vertex opposite the side chosen as the base is sometimes called the apex of the triangle .
- A triangle has three hauteurs, three medians, three perpendicular bisectorand three angle bisectors.
- Altitudes:
The three altitudes determine the orthocenter of the triangle. - Medians:
The three medians intersect at the centre of gravity (the centroid) of the triangle. - Perpendicular bisectors:
The three perpendicular bisectors intersect at the centre of the circle circumscribed about the triangle. - Angle bisectors:
The three angle bisectors intersect at the centre of the circle inscribed in the triangle.
- Altitudes:
Formulas
- The formula to calculate the perimeter P of a triangle with sides a, b and c is: [latex]P=a+b+c[/latex].
- The formula to calculate the area A of a triangle with a base b and an altitude h is: [latex]A=\dfrac{b × h}{2}[/latex].
- Heron's formula can be used to calculate the area A of a triangle given the lengths of the three sides, where s is the semiperimeter of the triangle: [latex]A=\sqrt{s(s\space –\space a) (s\space –\space b) (s\space –\space c)}[/latex].
Examples
