Question

An equilateral triangle is inscribed in a circle of radius 14cm.find the area between the circle and the triangle​

Answer 1

area of triangle is 1/2 bh

= 1/2 *14*14 = 196/2 = 98cm²

are of circle is πr² = 22/7 *14*14

= 22*196/7

= 616cm²

616-98 = 518cm²

Answer 2

Given:

The radius of the circle=14cm

To find:

The area between the circle and the triangle​

Solution:

The area between the circle and the triangle​ is 361.40$cm^{2}$.

We can find the area by following the given steps-

We know that the triangle inscribed in the circle is equilateral.

Let the side of the equilateral triangle be A.

We know that the altitude and the median of an equilateral triangle are the same and the centre of the circle divides it in the ratio of 2:1.

The altitude of the triangle=$\sqrt{3}$A/2

Now, this altitude is divided into 2:1 by the centre of the circle.

So, 2/3 of the altitude=radius of the circle

2/3×$\sqrt{3}$A/2=14

A/$\sqrt{3}$=14

A=14$\sqrt{3}$cm

Now that we have the side of the equilateral triangle, we can calculate the area of the triangle.

Area of the equilateral triangle=$\sqrt{3}$/4×$A^{2}$

On putting the value  of A, we get

=$\sqrt{3}$/4×14$\sqrt{3}$×14$\sqrt{3}$

=14×3×14$\sqrt{3}$/4

=7×3×7$\sqrt{3}$

=147$\sqrt{3}$

=254.60 $cm^{2}$

Similarly, the area of the circle=π$r^{2}$, r is the radius of the circle.

=22/7×14×14

=22×28

=616$cm^{2}$

Now, the area between the circle and the triangle=Difference between the area of the circle and the area of the triangle

=616-254.60

=361.40$cm^{2}$

Therefore, the area between the circle and the triangle​ is 361.40$cm^{2}$.