All the four vertices of a rhombus are on a circle of area 2826 cm^2. Find the area of rhombus (pi=3

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28 Jun 2013 Circle

All the four vertices of a rhombus are on a circle of area 2826 cm^2. Find the area of rhombus (pi=3.14)

OPtion

1) 1000 cm^2
2) 1200 cm^2
3) 1400 cm^2
4) 1600 cm^2
5) 1800 cm^2
6) 2000 cm^2
7) 2200 cm^2
8) 2400 cm^2
9) 2600 cm^2
10) None of these

Solution

The rhombus here is a square. As the rhombus is cyclic, cum of opposite angles is 180 degree, which are equal. So, each angle is 90 degree and the rhombus is a square.
Area of circle = 2826 cm^2
pi*r^2=2826 (let the radius of circle be r)
r=30 cm
Each diagonal = 2r
Area of square = 1/2 (D)^2
solve
ans 1800 cm^2
option 5

Correct Option: 5 Best Solution (9)

Ann Mary Jolly   11 years AGO

The rhombus inscribed in a circle is a square.
The diagonals of this square perpendicularly bisect each other at the centre of the circle.
Looking the geometry,we get to know that any side of the square,and the twoline segments from the ends of this side to the centre make a right triangle.
If the radius of the circle is r,
Then we get a side of the square = 2^(1/2)*r
From given, pi*(r^2) = 2826
=> r^2 = 2826/pi
Area of the rhombus = area of square
= side^2 = 2(r^2)
= 2*(2826/pi)
= 2*900 = 1800 cm^2

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Anil Kumar Bharti   11 years AGO

Exp:
Area of circle=Pi*r^2
2826=3.14*r^2
now r^2=900
then r=30
Now, Area of Rhombus=1/2*d1*d2
=1/2*60*60
=1800 cm^2

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Murali Krishna   11 years AGO

area of circle = pi*r^2=2826
r^2=900
area of rhombus=1/2(sides of diaognals)=1/2(2r)(2r)
=2*r^2

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krishnapriya   11 years AGO

given area of circle=2826
therefore,pi*r^2=2826
r^2=900
using pythagorus theorem,
2x^2=r^2=900
x=15sqrt(2)
Area of rhombus=(30sqrt(2))^2
=1800 cm^2

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Dhivya   11 years AGO

The area of rhombus is 1/2(d1*d2)
the four sides of rhombus are touching the circle the radius of circle is 30 cm
so the diagonal will be same i.e 60 cm
so the area of rhombus is 60*60/2= 1800cm^2

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Angeline   11 years AGO

The area of Rhombus is 1/2(d1*d2)
the four sides of rhombus are touching the circle the radius of circle is 30 cm
so the diagonal will be same i.e 60 cm
so the area of rhombus is 60*60/2= 1800cm^2

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Adarsha Upadhya   11 years AGO

area of circle=Pi*r^2
area of Rhombus=(d1d2)/2
2826=Pi*r^2
r=30 d=2r=60

area of Rhombus=(60*60)/2=1800cm^2

Like? Yes (2) | No (1)  

Parry   11 years AGO

area of circle=pi*r^2
2826=3.14*r^2
900=r^2
r=30

x^2 *x^2=30^2
2X^2=900
x=21.21
R=21.21*2
A=(899.72)^2
A=1800

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anand s idagal   11 years AGO

2826=πR^2
R=30
900×(√2)^2=1800

Like? Yes (1) | No (1)