Question

Find the area of a circle inscribed in an equilateral triangle of side $18cm$. [Take $\pi =3.14$]

• A. $84.78$ $c{m}^2$
• B. $85.78$ $c{m}^2$
• C. $86.78$ $c{m}^2$
• D. $87.78$ $c{m}^2$

Answer 1

Answer: (A)

$84.78$ $c{m}^2$

Let the radius of the circle be $r$ , this circle also inscribed the equilateral triangle of side $a$ = 18 cm

so from the relation between radius and side of triangle we get( hint: find by drawing the diagram :) )

Thus, $r=\frac{18}{2\sqrt{3}}$ cm
Area of the circle $=\pi (\frac{18}{2\sqrt{3}}{)}^2$
$=3.14\times \frac{324}{12}$
$=84.78c{m}^2$