Question 136

When a piece of wire is bent in the form of equilateral triangle then the area of the triangle is $$121 \sqrt{3} cm^{2}$$. If the same piece of wire is bent in the form circle , then the area of the circle in square centimeters is (Take $$\pi = \frac{22}{7})$$

Solution

we know that the area of the eqitriangle = $$a^{2}$$ $$\times$$ $$\sqrt{3}$$ \4 = $$121 \sqrt{3}$$

a = 22

then the length of the wire = perimeter of the triangle 

                                         = 3a = 3*22 = 66

then the radius of the circle = 2$$\pi$$r = 2*$$\frac{22}{7})$$*r = 66 

r = 21\2  

then area of the circle =  $$\pi$$ $$\times$$ $$r^{2}$$ =  $$\frac{22}{7})$$  $$\times$$ $$\frac{21}{2})$$  $$\frac{21}{2})$$

then area of the circle = 346.5 cm square  Answer 


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