Question

find the area of a circle inscribed in an equilateral triangle of side 18 cm

Answer 1

Answer:

Step-by-step explanation:

Radius of incircle=9/2√3

18/2√3=9√3cm

A=πr^2

=3.14×9/√3×9/√3

3.14×81/3

=3.14×27

=84.78cm

Answer 2

Given,

A circle is inscribed in an equilateral triangle of side 18 cm.

To find,

Area of the inscribed circle.

Solution,

We can solve this problem simply by following the below process.

So the largest circle that can be inscribed in a triangle is called the incircle, and the radius of this circle is known as the inradius.

For an equilateral triangle, the relation between the inradius and side of the triangle is given as follows,

$inradius=\frac{side}{2\sqrt{3}}$

With the help of the above relation, the inradius for the given circle will be,

$inradius (r)=\frac{18}{2\sqrt{3} }=\frac{9}{\sqrt{3} }=3\sqrt{3}$

⇒ inradius (r) = 3√3 cm

Now, the area of the incircle (let A), will be,

A = πr²,

where, r is inradius.

⇒ A = π(3√3)²

⇒ A = 3.14*(27)  [Taking π = 3.14]

⇒ A = 84.78 cm².

Therefore, the area of the given incircle will be 84.78 cm².