What is the Formula for a Triangles Area

What is the Formula for a Triangles Area

Introduction :

             The triangle is one which has a vertices of sides P,Q and R. If a line is drawn parallel to one side of a triangle then it intersects the other two sides in distinct points. Then the other two sides are in the same ratio. If we divide a line of any two sides in the triangle of equal ratio, then the line is parallel to the third side.

 

Concepts and formula for Area of a Right Angled Triangles:

 

The triangles are classified in terms of its angle as given below:-

  • Acute angled triangle.

  • Right angled triangle.

  • Obtuse angled triangle.

         The formula for the area of a rectangle has already been derived. We know that each angle of a rectangle is a right angle and its opposite sides are equal. We will try to obtain the area of a right triangle by using the information that the area of a rectangle in the product of its length and breadth.

  • Area of triangle =1 / 2 x base x height.

            ABCD is a rectangle. The diagonal BD are divides into two right triangles ABD a BCD, the hypotenuse is common to both the triangles and the sides containing right are also congruent in both the triangles. Therefore by (SSS) congruence both the triangles are congruent.

Area of the triangle ABD =Area triangle BCD....... (i)

The area of the rectangle ABCD = [ABD + BCD]....... (ii)

The area of the rectangle ABCD= the area of 2 triangle ABD

[From Eqn. (i) and (ii)]

The area of Triangle ABD = Area of the rectangle ABCD / 2

                                     = (AB x AD) / 2

When AB is the base of the Triangle ABD. Side AD is the perpendicular of the  Triangle ABD.

The formula for the area of a right triangle ABD = (Base x Perpendicular height) / 2

 

The formula and concepts Area of an Acute and Obtuse Angled Triangles:

 

The formula and concepts Area of an Acute and Obtuse Angled Triangles are as follows:

  • The Area of an Acute Angled Triangle:

The area of triangle ABC = The Area of the right triangle(Triangle ABD + triangle  ADC)

                                       = 1/2 BD × AD+ 1 / 2 DC × AD

                                       = 1/2 [BD + DC] × AD

                                       = 1/2 [BC × AD]

The formula is

                                       = 1/2 [Base × Altitude]

 

  • The Area of an Obtuse Angled Triangle:

 Area of the obtuse triangle ABC = Area of the right triangle ABD - area of the right triangle ACD

                                                = 1/2 [BD × AD] - 1/2 CD × AD

                                                = 1/2 [BD - CD] × AD

                                                = 1/2 [BC × AD]

The formula is

                                                = 1/2 [base × Altitude]

We can calculate the formula for area of any triangle if its base and height be given.

Therefore the formula is

  • The area of any triangle = 1/2 [base× height]