Question

The perimeter of an equilateral triangle is 72m.find it's area

Answer 1

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Question :

The perimeter of an equilateral triangle is 72m.find it's ar

Solution :

In the attachment

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Remember :

Equilateral angle is always = .

Answer 2

Answer:

Equilateral triangle is the triangle all of whose sides are equal. Let a

be the side of that triangle, then

P = a + a + a = 3a = 72

whence

a =  72 = 24m.

      3  

Recall that the area of a triangle with sides a, b and the angle α between them

is equal to

A =  1  ab sin α.

     2

The angle between any two sides of such an equilateral triangle is π

                                                                                                                3

, whence its  are a is equal to

A =  1  a · a · sin  π = 1  · 24 · 24 ·  √3  = 144√  3m2

     2                 3    2                    2