Math, asked by imlirenlajamir934, 4 months ago

A wire is bend to form an equilateral triangle . if the triangle is 4 root 3 cm², what is the area of a circle formed ( in cm²)by the same wire?

Answers

Answered by VineetaGara
1

Given,

A wire is bent to form an equilateral triangle.

The area of the equilateral triangle formed = 4√3 cm^2

To find,

The area of a circle formed (in cm²) by the same wire.

Solution,

We can simply solve this mathematical problem using the following process:

Let us assume that the length of each equal side of the equilateral triangle is x cm and the radius of the circle formed is y cm, respectively.

As per mensuration;

Area of an equilateral triangle= √3/4 (each equal side)^2

The perimeter of an equilateral triangle= 3×(each equal side)

Area of a circle = π(radius)^2

The perimeter of a circle = 2π(radius){Statement-1}

Now, according to the question;

The same wire is used to make an equilateral triangle and also a circle

=> the perimeter of the equilateral triangle = the perimeter of the circle

{Equation-1}

Now, according to the statement-1;

Area of the equilateral triangle = 4√3 cm^2

=> √3/4 (each equal side)^2 = 4√3 cm^2

=> (each equal side)^2 = 4cm^2 × 4

=> each side of the equilateral triangle = 4 cm

Now, according to statement-1;

The perimeter of the equilateral triangle formed

= 3×(each equal side)

= 3×(4 cm)

= 12 cm

=> the perimeter of the circle formed by the same wire = 12 cm

{according to equation-1}

=> 2π(radius) = 12 cm

=> radius of the circle formed = (6/π) cm

Now, the area of the circle formed

= π(radius)^2

{according to statement-1}

= π(6/π)^2 cm^2

= 36/π cm^2

= (36×7)/22 cm^2

= (252/22) cm^2

= 11.45 cm^2

Hence, the area of the circle formed is equal to 11.45 cm^2.

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