Let there be an equilateral ABC

18.jpg

We need to find its area

 

We know that,

  Area ∆ABC = 1/2 × Base × Height

 

Finding base & height of equilateral triangle ABC

Height is perpendicular from the vertex to the base.

 

Let us draw perpendicular from point A

19.jpg

So,

      Height = AD

      Base = BC = a

 

So, we need to find height AD

 

In equilateral triangle,

altitude is also the median

 

So, point D is also the mid-point of BC

 

Therefore,

  BD = DC = a/2

 

Now, in ∆ADC

By Pythagoras theorem

  AC 2 = AD 2 + DC 2

 

  a 2 = AD 2 + (a/2) 2

22.jpg

a 2 = AD2 + a 2/4

      AD^2 + a2/4 = a 2

     AD^2 = a2- a 2/4

    AD^2 = (4a 2   - a2   )/4

   AD^2 = (3a2 )/4

  AD = √((3a 2   )/4)

  AD = a/2 √3

  AD = (√3  a)/2

 

Now,

  Height = AD

= √3/2 a

  Base = BC

= a

Area of ∆ABC = 1/2 × Base × Height

= 1/2 × a × √3/2 a

= √3/4 a^2

∴ Area of equilateral triangle = √3/4 a 2

 

Find area of the following equilateral triangle whose sides are 2 cm

23.jpg

Side = a = 2 cm

Area of equilateral ∆ABC = √3/4 a 2

= √3/4 (2) 2

= √3/4 × 4

= √3 cm 2

 

∴ Area of equilateral triangle ∆ABC is √3 cm 2

 

 

  1. Chapter 11 Class 7 Perimeter and Area
  2. Concept wise

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.