Question

A wire is bent to from an equilateral triangle. If the area of the triangle is 4√3cm2, what is the area of the circle grimes by the same wire?​

Answer 1

Given :-

A wire is bent to from an equilateral triangle. If the area of the triangle is 4√3cm²

To Find :-

Area of circle

Solution :-

We know that

Area of equilateral triangle = √3/4 a²

√3a²/4 = 4√3

a² = 4√3 × 4/√3

a² = 4 × 4

a² = 16

a = √16

a = 4

Now

Length of the wire = 3a = 3(4) = 12 cm

Circumference of circle = 2πr

12 = 2 × 22/7 × r

12 × 7/2 × 22 = r

6 × 7/22 = r

42/22 = r

21/11 = r

Area of circle = πr²

Area = 22/7 × (21/11)²

Area = 22/7 × 441/121

Area = 11.45 cm²

Answer 2

Given information

• ↠ Wire is bent to from an equilateral triangle
• ↠ The area of the triangle is 4√3cm²

What we have to calculate

• ↠ We have to calculate the area of the circle grimes by the same wire

How we calculate

• ↠ Frist we will calculate the area of triangle [√3/4(side)²]
• ↠ After getting area of triangle we will multiply by length of wire
• ↠ Then we will calculate circumference of circle (2πr) where π = 22/7
• ↠ At last we will calculate Area of circle (πr²)

Let us calculate Area of triangle

❍As we know to Formula of area of equilateral triangle =√3/4(side)²

• Submitting values

➺ √3/4(side)² = 4√3(given)

• transferring sides

➺(side)² = 4√3 × 4/√3

• 4/√3 will get reciprocate

➺ (side)² = 4 × 4

• √3 will get canceled by √3

➺(side)² = 16

• On multiplying 4 by 4

➺ side = √16

• rooting both the sides

➺side = 4

Finding length of wire

• As we know triangle have 3 face

➺lengths = 3(side )

• putting value

➺lengths = 3(4)

• On multiplying

➺ Length = 12cm

Length of wire is 12cm

Finding circumference of circle

To calculate the circumference of a circle, multiply the diameter of the circle with π (pi). The circumference can also be calculated by multiplying 2×radius with π

➺circumference of circle = 2πr

• Submitting values

➺ 12 = 2× 22/7 × radius

• On multiplying

➺12 = 44/7 × radius

• transferring sides

➺ radius = 12 × 7/44

• on multiplying

➺radius = 84/44

• Dividing 84 by 44

➺radius = 42/22

• Dividing 42 by 22

➺radius = 21/11

Radius of a circle is 21/11

Finding area of circle

The area of a circle is pi times the radius squared (A = π r²).

➺Area of circle = πr²

• putting value

➺Area of circle = 22/7 × (21/11)²

• opening brackets

➺Area of circle = 22/7 × 21/11 × 21/11

• Multiplying denominator

➺Area of circle = 22 × 21 × 21 /847

• On multiplying

➺Area of circle = 9,702/ 847

• on Dividing

➺Area of circle = 11.45cm²

The area of circle us 11.45cm²