# The Triangle

**Definition of a Triangle**

Triangle is a closed figure bounded by three straight lines called sides. It can also be defined as polygon of three sides.

**Area of triangle**

The area of the triangle is given by the following formulas:

$A = \frac{1}{2}bh$

Given two sides and included angle

$A = \frac{1}{2}ab \sin \theta$

Given three sides (see the derivation of Hero's formula)

$A = \sqrt{s(s - a)(s - b)(s - c)}$

where, $s = \frac{1}{2}(a + b + c)$ called the semi-perimeter.

Given one side and three angles (say angles A, B, and C, and side b are given)

$Area = \dfrac{b^2\sin A~\sin C}{2\sin B}$

See also the links below: