Question

A wire is bent to form an equilateral triangle. If the area of the triangle is 4√3 cm², what is the area of the circle formed (in cm²) by the same wire?
1. 6/π
2. 12/π
3. 36/π
4. 48/π
​

Answer 1

Answer:

therefore option (c) is correct

Answer 2

$\text{ \bf \: Area \: of \: circle} \: \bf=\: \frac{36}{ {\pi} } \: {cm}^{2}$

Option 3 is correct.

Given:

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

To find:

• What is the area of the circle formed (in cm²) by the same wire?

1. 6/π
2. 12/π
3. 36/π
4. 48/π

Solution:

Formula to be used:

• Area of equilateral triangle=$\bf \frac{ \sqrt{3} }{4} {a}^{2}$; where 'a' is side of equilateral triangle

• Perimeter of equilateral triangle$= 3a$
• Area of circle $= \pi {r}^{2}$
• Circumference of circle $= 2\pi \: r$

Step 1:

Area of equilateral triangle is 4√3 cm².

Let the side of equilateral triangle is 'a' cm

$\frac{ \sqrt{3} }{4} {a}^{2} = 4 \sqrt{3}$

or

${a}^{2} = 16$

or

$\bf a = \pm \: 4$

(-ve) value of side must be discarded.

So,

Length of each side of equilateral triangle is 4 cm.

Step 2:

Find Perimeter of triangle.

Perimeter of equilateral triangle is = 3×4

Perimeter of equilateral triangle is= 12 cm

Step 3:

As length of wire is 12 cm.

Thus,

Circumference of circle is 12 cm.

So,

$2\pi \: r = 12$

or

$r = \frac{12}{2\pi}$

or

$\bf r = \frac{6}{\pi} \: cm$

Step 4:

Find Area of circle.

As radius is r= 6/π cm

$\text{Area \: of \: circle} = \pi \: \left({ \frac{6}{\pi} } \right)^{2}$

or

$\text{Area \: of \: circle} = \pi \: \frac{36}{ {\pi}^{2} }$

or

$\text{\bf Area \: of \: circle} \bf=\: \frac{36}{ {\pi} } \: {cm}^{2}$

Thus,

Option 3 is correct.

Learn more:

1) Find the circumference of a circle whose radius is 49 cm.

https://brainly.in/question/4140113

2) the area of a semicircle of diameter 42 cm is

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