Question

vertices of a rhombus is on one circle. If area of the circle is 1256 cm^2, then find area of rhombus.(take π=3.14)​

Answer 1

Step-by-step explanation:

Let r be the radius of circle.

Given that,

Area of circle = 1256 cm²

πr² = 1256

$⟹ \tt \red{{r}^{2} = \frac{1256}{\pi} }$

$⟹ \tt \red{{r}^{2} = \frac{1256}{314}}$

$⟹ \tt \red{{r}^{2} = 400}$

$⟹ \tt \red{{r}^{2} = (20 {)}^{2} }$

$⟹ \tt \red{r = 20 \: cm}$

$∴ \tt\: So, \: the \: redius \: of \: circle \: is \: 20 \: cm$

$⟹ \tt{Diameter \: of \: circle = 2 \times Radius }\\ \\ \: \: \tt{= 2 \times 20} \\ \\ \: \: \tt{= 40 \: cm}$

Since, all the vertices of a rhombus lie on a circle that means each diagonal of a

$\tt{Let \: d\frac{}{1} \: and \: d \frac{}{2 } \: be \: the \: diagonal \: of \: the \: rhombus.}$

$∴ \tt{ \: d \frac{}{1} \: and \: d \frac{}{2} = Diagonal \: of \: circle = 40 \: cm}$

$\tt \red{So, Area \: of \: rhombus = \frac{1}{2} \times d \frac{}{1} \times d \frac{}{2} }$

$\tt \red{ = \frac{1}{2} \times 40 \times 40}$

$\tt \red{ = 20 \times 40}$

$\tt \red{ = 800 {cm}^{2} }$

Answer:-

$\tt \red{Hence \: the \: required \: Area \: of \: rhombus \: is \: 800 {cm}^{2} }$

Answer 2

The required area of rhombus is 800 cm^2