If a square and a rhombus stand on the same base, then the ratio of the area of the square and the r

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29 Sep 2015 Area

If a square and a rhombus stand on the same base, then the ratio of the area of the square and the rhombus is

OPtion

1) Greater than 1
2) Equal to 1
3) Equal to 1/2
4) Equal to 1/3
5) Equal to 1/4
6) Less than 1
7) Equal to 1/5
8) Equal to 2/3
9) Equal to 3/4
10)None of these

Solution

Area of square = a^2 where a is base length
Area of rhombus with same base = a * h where h is perpendicular height. This height can be changed from a to 0 so definitely area on square will be more than area of rhombus.

Option 1)

Correct Option: 1 Best Solution (20)

kriti kankariya   9 years AGO

ar. of sq = a^2
ar. of rombus = a^2 * sinA
so its ratio will become
ar. of sq/ar. of rombus = 1/sinA
and sinA will lie btw 0 to 1
so the ratio will be > 1

Like? Yes (22) | No (9)  

Aman   9 years AGO

Consider a square and rhombus standing on the same base 'a'. All the sides of a square are of equal length. Similarly all the sides of a rhombus are also of equal length. Since both the square and rhombus stands on the same base 'a',

Length of each side of the square = a
Length of each side of the rhombus = a

Area of the sqaure = a2 ...(1)

From the diagram, sin θ = ha
=> h = a sin θ

Area of the rhombus = ah = a × a sin θ = a2 sin θ ...(2)

From (1) and (2)

Area of the squareArea of the rhombus=a2a2sinθ=1sinθ

Since 0° < θ < 90°, 0 < sin θ < 1. Therefore, area of the square is greater than that of rhombus, provided both stands on same base.

Like? Yes (8) | No (3)  

aditi kumari   9 years AGO

RATIO=(area of sqr)/(Area of rhombus)
=((side)^2)/(product of adjacen side * sine of angle between two sides).

Like? Yes (13) | No (9)  

siddhi datri   9 years AGO

Let the common side be a.
Then altitude of rhombus will be less than a
So, Ar(square)/Ar(rhombus)=a^2/a*(less than a)
=>Ar(square)/Ar(rhombus)>1

Like? Yes (9) | No (6)  

priya   9 years AGO

ratio of square/rhombus is a*a / (a*a*square root of 2 )/2 = 1.414

Like? Yes (6) | No (4)  

RUPNARAYAN RANA   9 years AGO

Let the base of square and rhombus be a units . Square all sides equal ; Area of square=a^2,
let the height of rhombus , i.e perpendicular distance from the top edge to the base be h units and included angle be x
then area of rhombus =a*h=a^2sinx
ratio = (a^2)/(a^2*sinx) = 1/sinx and since 0

Like? Yes (3) | No (2)  

ABHIJEET ANAND   9 years AGO

area of sqare/area of hombus=(1/sina).
where a is the interior angle which is less than 90 deg.
so sina1.
so ratio>1.

Like? Yes (2) | No (2)  

Ajay Kumar Gupta   9 years AGO

If a square and a rhombus lie on the same base, area of the square will be greater than area of the rhombus (In the special case when each angle of the rhombus is 90°, rhombus is also a square and therefore areas will be equal)

Like? Yes (2) | No (3)  

sudiptaa   9 years AGO

If a square and a rhombus lie on the same base, area of the square will be greater than area of the rhombus (In the special case when each angle of the rhombus is 90°, rhombus is also a square and therefore areas will be equal)

Like? Yes (3) | No (4)  

Dwaipayan Goswami   9 years AGO

Let the base of square and rhombus be a units . In square all sides are equal.let's 'a' be the base shared by both square and rhombus. Area of square=a^2. let the height of rhombus. i.e, perpendicular distance from the top edge to the base be h units and included angle be x
then area of rhombus =a*h=a^2sinx
ratio = (a^2)/(a^2*sinx) =1/sinx and since 0

Like? Yes (2) | No (3)  

Aman Jain   9 years AGO

let side of rhombus = x
and side of square is also =x
sin theta=h/x
h=asin theta

area of rhombus=ah
=a*asin theta ->a2 sin theta.......1
are of square =a2......2
from eq 2 and 1
area of square/area of rhombus==a2/a2sin theta
==1/sin theta
thats why

Like? Yes (1) | No (2)  

Pesari Udayasree   9 years AGO

answer:1
area of square of side a is a^2
area of rhombus is a^2 sinA
there ratio is a^2 ÷a^2sinÀ=1÷sinA
as A lies between 0° to 90°,sinA lies between 0 to 1. therefore there ratio is greater than 1.

Like? Yes (2) | No (3)  

praveendas   9 years AGO

area of the rhombu is less than the area of the square
then the ratio will become greater than1

Like? Yes (2) | No (3)  

Anup Sahay   9 years AGO

let a be the side of square
so, area of square=A1= a*a
area of rhombus =A2==1/2*a*a
A1/A2= 2/1
so option 1

Like? Yes (7) | No (8)  

Shubham Raj   9 years AGO

Area of the sqaure = a2 ...(1)

From the diagram, sin θ = ha
=> h = a sin θ

Area of the rhombus = ah = a × a sin θ = a2 sin θ ...(2)

From (1) and (2)

Area of the square Area of the rhombus=a^2 /a^ 2sin
=1 sinθ

Since 0° < θ < 90°, 0 < sin θ < 1.
Therefore, area of the square is greater than that of rhombus, provided both stands on same base.

Like? Yes (1) | No (2)  

chinu singla   9 years AGO

Length of each side of the square = a
Length of each side of the rhombus = a

Area of the square = a^2 ...(1)
as base=a and height=h so,
sinθ = h/a
=> h = a sin θ

Area of the rhombus = ah = a × a sin θ = a^2 sin θ ...(2)

From (1) and (2)

Area of the square/Area of the rhombus=a^2/a^2sinθ=1/sinθ

Since 0° < θ < 90°, 0 < sin θ < 1. Therefore, area of the square is greater than that of rhombus, provided both stands on same base.

Like? Yes (1) | No (2)  

akhil sharma   9 years AGO

if x is side of sqre then ratio will be x^2 /x^2-(area of triangle left )+(area of triangle added)
which is equals to 1

Like? Yes (1) | No (2)  

Nandkishor jaiswal   9 years AGO

If a square and a rhombus lie on the same base, area of the square will be greater than area of the rhombus (In the special case when each angle of the rhombus is 90°, rhombus is also a square and therefore areas will be equal)

Like? Yes (3) | No (4)  

ROHIT   9 years AGO

f a square and a rhombus lie on the same base, area of the square will be greater than area of the rhombus (In the special case when each angle of the rhombus is 90°, rhombus is also a square and therefore areas will be equal)

Like? Yes (3) | No (4)  

himanshu mishra   9 years AGO

Rhombus and square both have same side length, if they standing in the same base area will be same

Like? Yes (2) | No (4)