Question

Prove that the area of a equilateral triangle with side a=√3/4 a². please solve it in details. in copy​

Answer 1

area of equilateral triangle √3/4a²

Answer 2

Answer:



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Class 7

>>Maths

>>The Triangle and Its Properties

>>Isosceles and Equilateral Triangles

>>In an equilateral triangle with side ' a

Question



In an equilateral triangle with side 'a', prove that the area of the triangle is 43a2.

Medium

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Solution



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Proof- Since all the 3 sides of an equilateral triangle are same AB=BC=CA=a

For altitude of △ABC

Draw a ⊥ from point C on AB.

So that CO⊥AB. Let OC=h

In △AOC

By using Pythagoras Theorem

AC2=AO2+OC2

OC2=AC2−AO2

h2=a2−(2a)2

h2=a2−4a2

h2=43a2⇒h=23