Question

a piece of wire is bent in the shape of equilateral triangle of side 4.4cm. If this wire is rebent to form of a circle , find the radius and the area of the circle. pls say how you found the radius

Answer 1

${\huge{\underline{\underline{\rm{Question:-}}}}}$

A Piece of wire is bent in the shape of equilateral triangle of side 4.4 cm . If this wire is re bent to form of a circle . Find the radius and the area of the circle .

${\huge{\underline{\underline{\rm{Answer\checkmark}}}}}$

★ Given :

• The wire is same in both cases.
• Side of equilateral ∆ = 4.4 cm .
• It's re bent and made a circle .

★ To Prove :

• Radius of the circle
• Area of the circle

★ Solution :

Since , the wire is same , so , the length of the wire would be same .

# Finding the perimeter of equilateral triangle .

$\mapsto \rm \: perimeter \: of \: equilateral \triangle = 3 \times side$

$\mapsto \rm \: perimeter = 3 \times 4.4 \: cm$

$\leadsto \boxed{\rm \: perimeter = 13.2 \: cm \: }$

As , the length of the wire is same ,

so ,

$\mapsto \rm \: perimeter \: of \: \triangle = circumference$

$\mapsto \rm \: 13.2 \: cm = 2 \pi \: r$

$\mapsto \rm \: \cancel{13.2} \: cm = 2 \times \frac{ \cancel{22}}{7} \times r$

$\mapsto \rm \: \cancel{0.6} \: cm \: = \cancel2 \times \frac{r}{7}$

$\mapsto \rm \: 0.3 \: cm \times 7 = r$

$\leadsto \pink{\boxed{\rm \: r = 2.1 \: cm}}$

Now , finding area .

$\mapsto \rm \: area = \pi {r}^{2}$

$\mapsto \rm \: area = \frac{22}{7} \times {(2.1)}^{2} \: {cm}^{2}$

$\mapsto \rm \: area = \frac{22}{ \cancel7} \times \cancel{2.1} \times 2.1 \: {cm}^{2}$

$\mapsto \rm \: area = 22 \times 0.3 \times 2.1 \: {cm}^{2}$

$\leadsto \purple{ \boxed{ \rm \: area = 13.86 \: {cm}^{2} \: }}$

So ,

Final answer :

• Radius of circle = 2.1 cm
• Area of circle = 13.86 cm²

_________________________

★ Know More :

# The unit of area is always in the type : unit²

# Perimeter of circle = 2πr

# Area of circle = πr²

# Perimeter of any triangle = sum of all sides

# Area of any triangle = $\dfrac{1}{2}$ × base × height