Area of Triangles

Let's learn about the area of Triangle. Let's start with the basics.

1. Right triangle and Triangle with a height.

Area of both triangles equals: A = h * c / 2

Let's prove for the second triangle (the first one can be proved similarly):

Area(ADC) = h*(d+c)/2, which is half area of rectangle with sides d+c and h

Area(ADB) = h*d/2, which is half area of rectangle with sides d and h

Area(ABC) = Area(ADC) - Area(ADB) = h*(d+c)/2 - h*d/2 = h*c/2

Thus, Area(ABC) = h*c/2

2. Triangle with two sides and angle

A = b*c*sin(A)/2

Let's prove it:

Draw a height,

A = b * c * sin(A)/2

sin(A) = opposite/hypotenuse = h / b

thus,

A = b * c * (h/b) /2

which  can be simplified to:

A = c * h / 2 and this formula we've proved above.

The End.