Latest Elitmus Aptitude Question SOLUTION: there is a equilateral triangle whose area is A.another triangle is formed by joining the mid points.this process is continued.find the sum of these areas.

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there is a equilateral triangle whose area is A.another triangle is formed by joining the mid points.this process is continued.find the sum of these areas.

Asked In Elitmus joshna rani mahapatra (8 years ago)

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Bikash kumar  (8 years ago)

Area of equilateral triangle =(root(3)/4)*a^2=A(given)
side of triangle=a
now side is a/2
then total area A+A/4 +A/16-------
A/1-(1/4)=A*4/3 is total area

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Ashok Kumar Thakur  (8 years ago)

Ans:- the answer is 4
Explanation:- Area of Equilateral triangle formed by joining the mid point of an equilateral triangle is 1/4 th of the original triangle .
So this will form an infinite GP series with common ratio 1/4 and first term =3
So the Sum will be
3/(1-1/4)=4

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Arvind kumar yadav  (8 years ago)

let the area of the eqilateral tringle=A
so, the area of the tringle joining the mid point of the sides=1/4A
and this process is continued.......... means tends to infinity..
so, this is geometry progression with infinite terms.....
A+1/4 A+1/16 A+...............infinite terms
whose first term a=A
common ratio r= 1/4

Now we can use the formula of the geometry progression s= a/(1-r)
putting the value in this equation we get ,

A/(1-1/4)
= 4/3 A is the right ans

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rohit pandey  (8 years ago)

Let ABC is an equilateral triangle with area = A
Remember: The area of the triangle formed when mid points of the triangle is joined is exactly one-fourth of the bigger triangle. So Area of DEF = A/4. Similarly Area of GHI = A/16 and so on ...
So Sum of the areas of all triangles = A+A/4+A/16+... ⇒A(1+1/4+1/16+...)
The series in the bracket is G.P. and S∞=a/1−r
⇒A(1/1−1/4⎞⎠⇒ ⇒4A/3

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