Question

If ABC is an equilateral triangle with side 12 cm, then the area of triangle formed by joined its mid points is: Quisq cm (A) 27 sqm (C) 64 sq cm (D) none of these​

Answer 1

Given : ABC is an equilateral triangle with side 12 cm,

To Find : the area of triangle formed by joined its mid points ​

Solution:

An equilateral triangle has all its sides of same length

Hence all the side lengths = 12 cm

line joining the mid-point of two sides of a triangle is equal to half the length of the third side

Length of each sides of Triangle formed = 12/2  = 6 cm

So new triangle formed is Equilateral Triangle

Area of an Equilateral triangle =  $\dfrac{\sqrt{3} }{4} (\text{side})^2$

Side length = 6 cm

Area of Triangle = $\dfrac{\sqrt{3} }{4} (\text{6})^2$

=> Area of Triangle = 9√3  cm²

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Answer 2

Answer:

An equilateral triangle has all its sides of same length

Hence all the side lengths = 12 cm

line joining the mid-point of two sides of a triangle is equal to half the length of the third side

Length of each sides of Triangle formed

12/2 = 6 cm

So new triangle formed is Equilateral Triangle

Area of an Equilateral triangle = √3,/4(side)²

Side length = 6 cm

Area of Triangle = √3/4 (6)²

= Area of Triangle = 9√3 cm²

Option A is the correct answer.