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Question

A wire when bent in the form of an equilateral triangle encloses an area of 1213 cm2. The same wire is bent to form a circle. Find the area enclosed by the circle.


Solution

Area of an equilateral Δ=34×a2 where a = side

Now, given that -

34×a2=1213

a2=121×4

a=11×2=22

Therefore, length of wire = a + a + a = 66

Now, this wire is bent into a circle, so the circumference of the circle =2πr=66

2×(227)r=66

r=212

Now, the area of this circle =πr2

=(227)×(212)2=6932=346.5cm²

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