Please wait...
1800-212-7858 (Toll Free)
9:00am - 8:00pm IST all days
For Business Enquiry


Thanks, You will receive a call shortly.
Customer Support

You are very important to us

For any content/service related issues please contact on this toll free number


Mon to Sat - 11 AM to 8 PM

Prove that the area of an equilateral triangle described on one side of a square is equal to half the area of the equilateral triangle described on one of its diagonals.

Asked by Topperlearning User 4th June 2014, 1:23 PM
Answered by Expert


Let ABCD be a square of side a.

Therefore its diagonal

Two desired equilateral triangles are formed as ABE and  DBF.

Length of one side of ABE = a

Length of one side of DBF

We know that equilateral triangles have all angles as 60o. So, all equilateral triangles are similar to each other.

So, ratio between areas of these triangles will be equal to the square of the ratio of their corresponding sides of these triangles.


Hence, proved.

Answered by Expert 4th June 2014, 3:23 PM
Rate this answer
  • 1
  • 2
  • 3
  • 4
  • 5
  • 6
  • 7
  • 8
  • 9
  • 10

You have rated this answer 8/10

Your answer has been posted successfully!

Chat with us on WhatsApp