Question

Question 12
All the vertices of a rhombus lie on a circle . Find the area of the rhombus, if area of the circle is $1256c{m}^2$. (use $\pi =3.14$)

Answer 1

Let the radius of the circle be r.

Given that, Area of the circle $=1256c{m}^2$

$\pi r^2=1256$

$\Rightarrow r^2=\frac{1256}{\pi }=\frac{1256}{3.14}=400$

$\Rightarrow r^2=(20{)}^2$

$\Rightarrow r=20cm$

$\therefore$ So, the radius of circle is 20 cm

$\Rightarrow$ Diameter of circle $=2\times Radius$

$=2\times 20$

$=40cm$

Since, all the vertices of a rhombus lie on a circle that means each diagonal of a rhombus must pass through the centre of a circle. This implies both the diagonal are equal and same as the diameter of the given circle.

Let $d_1$ and $d_2$ be the diagonals of the rhombus.

$\therefore d_1=d_2$ = Diamter of circle =40 cm

So, Area of rhombus $=\frac{1}{2}\times 40\times 40$

$=20\times 40=800c{m}^2$

Hence, the required area of rhombus is $800c{m}^2$