Question

a circle is circumscribed by the rhombus which in turn is made by joining the mid points of a rectangle whose sides are 12cm and 16cm respectively. what is the area of the circle

Answer 1

ans.
correct answer is

452.16

Answer 2

The area of the circle which is inscribed in a rhombus which in turn is inscribed in a rectangle is 72.41 cm².

Step-by-step explanation:

Referring to the figure attached below, we have  

ABCD is a rectangle with dimensions 16 cm x 12 cm.

Joining the midpoints E, F, G & H of the rectangle, a rhombus EFGH is formed.

Let HF and EG, the diagonals of the rhombus, be denoted as “d1” and “d2” respectively.  

From the figure we can say, AB = HF = 16 cm and BC = EG = 12 cm.

We know that the formula of the radius of a circle which is inscribed in a rhombus is given by,

Radius, r = $\frac{d1 * d2}{2 * \sqrt{d1^2 +d2^2} }$

Therefore, substituting the given values in the above formula, we get

r = $\frac{16 * 12}{2 * \sqrt{16^2 + 12^2}} = \frac{192}{2 * \sqrt{400} } = \frac{192}{2 * 20} = \frac{192}{40} = \frac{24}{5}$ = 4.8 cm

Thus, substituting the value of r, we get

The area of the circle inscribed inside the rhombus as,

= πr²

= (22/7) * (4.8)²

= (22/7) * 23.04

= 72.41 cm²

-------------------------------------------------------------------------------------------

Also View:

A circle is inscribed in a rhombus whose one angle is 60°. Find the ratio of area of the rhombus to the area of the inscribed circle.

https://brainly.in/question/1515370

Prove that rhombus inscribed in a circle is a square .

https://brainly.in/question/1209863

What is the length of ab 3 circles in a rectangle/ questions?

https://brainly.in/question/6951412