Area of triangle

Let us take triangle ABC

Let there be another triangle which is exactly same as ∆ABC

If we join both these triangles

We get a parallelogram ABCD

So, two equal triangles form a parallelogram

Now,

  Area of parallelogram = Base × Height

  Area of ∆ABC + Area of ∆DEF = b × h

Since both triangles are same,

their area will be equal

Area of ∆ABC + Area of ∆ ABC = b × h

                        2 Area of ∆ABC = b × h

    Area of ∆ABC = b × h

    Area of ∆ABC = 1/2 × b × h

So, our formula is

        Area of triangle = 1/2 × b × h

For right angled triangle ∆ABC

Height = h = AB

  Base = b = BC

So,

Area of ∆ABC = 1/2 × b × h

= 1/2 × AB × BC

Here,

  base is any side of triangle

          & height is perpendicular from opposite  vertex to the base

Let’s take some examples

Find area of Δ ABC

In ∆ABC,

Height = h = AD

  = 4 cm

Base = b = BC

= 5 cm

So,

Area of ∆ABC = 1/2 × b × h

= 1/2 × 5 × 4

= 5 × 2

= 10 cm ²

∴ Area of ∆ABC is 10 cm ²

Note: Here, height is outside the triangle

Find area

In ∆ABC,

Height = h = AD

  = 3 cm

Base = b = BC

= 4 cm

So,

Area of ∆ABC = 1/2 × b × h

= 1/2 × 4 × 3

= 2 × 3

= 6 cm ²

∴ Area of ∆ABC is 6 cm ²

Find area

In ∆ABC,

Height = h = BE

    = 4 m

  Base = b = AC

           = 8 m

So,

Area of ∆ABC = 1/2 × b × h

= 1/2 × 8 × 4

= 4 × 4

= 16 m ²

∴ Area of ∆ABC is 16 m ²

Find area

In ∆ABC,

Height = h = BE

  = 3 m

Base = b = AC

= 3 m

So,

Area of ∆ABC = 1/2 × b × h

= 1/2 × 3 × 3

= 1/2 × 9

= 9/2

= 4.5 m ²

∴ Area of ∆ABC is 4.5 m ²