Area of a Triangle

The symbol **Δ** is also used to represent the area of a triangle.

The basic formula for the area of a triangle is: **Δ = (1/2) × base × altitude**

For a right-angled triangle, the right angle (90°) is contained by the base and altitude. So if a, b, c are its sides and 'c' is the hypotenuse, then:

Area of a right-angled triangle,

(i) **Δ = (1/2) ab**

Also (ii) **Δ = (1/2) bc sin A = (1/2) ca sin B = (1/2) ab sin C**

(iii) **Δ =**

Note that formula (iii) for the area of a triangle is valid for any triangle.

(iv) **Δ = 2R**^{2} sin A sin B sin C

**Circumcenter and circumradius:**

In a triangle, the point of concurrence of the perpendicular bisectors of the sides is called as **circumcenter** (represented by 'O'). The circumcenter is equidistant from the three vertices.

i.e., OA = OB = OC = R (say)

So if we draw a circle with 'O' as center and R as radius, it passes through the three vertices. The circle is called circumcircle and '**R**' is called as **circumradius**.

The area of a triangle in terms of 'a', 'b', 'c and 'R' is: Δ = .