# Triangle

## 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.

### Formulas

• The formula to calculate the perimeter P of a triangle with sides a, b and c is: $$P=a+b+c$$.
• The formula to calculate the area A of a triangle with a base b and an altitude h is: $$A=\dfrac{b × h}{2}$$.
• 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: $$A=\sqrt{s(s\space –\space a) (s\space –\space b) (s\space –\space c)}$$.