A parallelogram has sides 60 m and 40 m and one of its diagonals is 80 m long. Then its area is

mohita verma   9 years AGO

by herons formula,
s=(1/2)(a+b+c)
s=(40+60+80)/2
s=90
area of //gm =2Xsqrt(90(90-60)(90-40)(80-80))
=2X300 sqrt(15)
=600 sqrt(15) m^2

Like? Yes (32) | No (5)  

Vivek   9 years AGO

Considering parallelogram as two symmetrical triangles with sides 40,60,80 metres
we have
Area of triange= Sqrt(s(s-40)(s-60)(s-80))
s=(40+60+80)/2=90
So area= Sqrt(90*(90-40)*(90-60)*(90-80))
=Sqrt(90*50*30*10)
=300*Sqrt(15)
Since there are two such triangle
Total area of parallelogram =2*300*Sqrt(15)
=600*Sqrt(15) m^2
Therefore the answer is 6)

Like? Yes (33) | No (9)  

Rakesh Kumar   9 years AGO

my answer is correct ,because first of all i find height and then calculate its area

Like? Yes (13) | No (3)  

viswambher   9 years AGO

let the parallelogram be divided into 2 similar triangles of side lengths a,b,c which are 40,60,80 respectively

area of 1 triangle = sqrt[s(s-a)(s-b)(s-c)]
where s= (a+b+c)/2
and area of the parallelogram is twice the area of the triangle which comes out to be 600sqrt(15)m^2

Like? Yes (13) | No (3)  

POOJA SINGH   9 years AGO

Let ABC be a triangle such that a=60m b=40m c=80m so s=(a+b+c)/2=90m
Then area of triangle=?s(s-a)(s-b)(s-c)=300?15m^2
So area of parallelogram=2*300?15=600?15m^2

Like? Yes (14) | No (6)  

anand vijay   9 years AGO

Let ABCD be a parallelogram where AB is parallel to CD
Let AC be one of its diagonal
then, ABC becomes triangle
where
AB = 60m, BC=40m and AC = 80m
s=1/2(60+40+80)m=90m
where s is the semi perimeter of the triangle
(s-a) = 30m, (s-b) = 50m and (s-c)=10m
calculating area of triangle when all the three sides are given using Heron's formula
Area of triangle ABC = Sqrt( s(s−a)(s−b)(s-c)) m^2
= Sqrt(90 * 30 * 50 * 10) m^2
= 300 Sqrt(15) m^2
Hence, area of ABCD =2* area of ABC
=600 Sqrt(15) m^2
option (6) is the right answer

Like? Yes (15) | No (9)  

manju   9 years AGO

Explanation:
AB = 60m, BC=40m or AC = 80m
s=1/2(60+40+80)m=90m
(s-a) = 30m, (s-b) = 50m and (s-c)=10m
Area of ΔABC = √s(s−a)(s−b)(s−c)
=√90×30×50×10m^2=300√15−−m^2
Area of //gm ABCD = 600√15m^2

Like? Yes (7) | No (1)  

sudiptaa   9 years AGO

s=(1/2)*(40+60+80)=90
area of ||gm=2*(sqrt(90*10*50*30))=600sqrt(15)

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RAJESH   9 years AGO

s=1/2(60+40+80)=90cm
s=1/2(s(s-a)(s-b)(s-c))
abc=300sq root 15 m^2
abcd=600sqroot15m^2

Like? Yes (6) | No (2)  

kanithi.shanmukharao   9 years AGO

ab=40m,bc=60m,ac=80m..
s=1/2(40+60+80)=90m
triangle ABC area=sqrt(s(s-a)(s-b)(s-c)=300sqrt15 m^2.
area of ||gm ABCD=600sqrt15 m^2

Like? Yes (5) | No (2)  

vamsi krishna   9 years AGO

sum of the areas of two triangles formed in parallelogram is
= 2*sqrt(s(s-a)(s-b)(s-c))
s=a+b+c/2

Like? Yes (4) | No (1)  

Chandrima Goswami   9 years AGO

angle A = arccos( (p2 - a2 - b2) / (-2ab) )=104.47 degree
other diagonal, q = √( a2 + b2 + 2ab cos(A) )=63.24 m
area K = ab sin(A)=2323.79 m^2= 600( sqrt15) m^2

Like? Yes (5) | No (2)  

Soma Naresh   9 years AGO

two sides 40, 60 with diagonal 80 of parallelogram makes two triangles of three sides 40, 60, 80
area of parallelogram becomes twice of the area of triangle
area of triangle with sides a, b and c is
sqrt (s (s-a)(s-b)(s-c))
s =(a+b+c)/2 =(40+60+80)/2=90
area= sqrt (90×50×30×10)
=sqrt (1350000)
=sqrt (90000×15)
=300sqrt(15)
area of parallelogram= 2×300 sqrt (15)
=600sqrt (15) m^2

Like? Yes (4) | No (1)  

Math Lovers   9 years AGO

AB=60 m =c, BC= 40 m=a, and AC=80m=b

now,

s= 0.5 *(40+60+80) = 90
Area of triangle ABC = sqrt {(s-a)(s-b)(s-c)}
=> A = 300 sqrt(15)
Area of Parallelogram = 2*300sqrt(15) = 600sqrt(15)

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SURAJ KUMAR   9 years AGO

diagonal^2= 40^2+60^2+2cosx
cosx=1/4
sinx=sqrt(15)/4
area=60*40*sqrt(15)/4
area=600sqrt(15)m^2

Like? Yes (6) | No (3)  

Ravi shankar   9 years AGO

considering half parallelogram a triangle is formed 3 side are given 40 ,60, 80.
applying herons formula for half triangle A=sqrt(p*(p-40)*(p-60)*(p-80)). where p=(40+60+80)/2=90.
ans==2*a= 600*sqrt(15)

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shubham shukla   9 years AGO

since, diagonal divides parallelogram into 45 degree angles.
so, area of parallelogram=(sum of area of two similar triangles)+(area of rectangle)
now,for triangles:
base=80cos45-40
from Pythagoras,height=square root{(60^2)-(base^2)}
now,for rectangle:
length=40-base of triangle
breadth=height of triangles
now, Area of parallelogram=2*{(1/2)*(16.568)*(57.66)}+{57.66*23.432}=23015.6m^2
so option(6)=600sqrt(15)=2315.6(approx.)

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prithwiraj banerjee   9 years AGO

drawing the diagram we get two equal triangle with sides of length 60m,40m,80m.
finding the area of each triangle and doubling it we get the area of the parallelogram.

Like? Yes (4) | No (1)  

syed kashif ullah   9 years AGO

s=(a+b+c)/2
s=90
apply herons formula
are of triangle=sqrt s(s-a)(s-b)(s-c)
=sqrt 90*30*50*10
=sqrt 1350000
=300 sqrt 15
area of parallelogram=2*300 sqrt 15
=600sqrt 15 square meter

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aditi goyal   9 years AGO

we can solve it using herons formula..
and calculate area of triangle i.e 300 sqrt (15) and doubling it we get option 6

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Shiva Sharma   9 years AGO

we find height and base*height is answer
now we find cosA
6400 = 3600+1600+2*40*60*cosA
cosA = 1/4
sinA=sqrt(15)/4
so sinA = height/hypotenuse
sqrt(15)/4 = height/40
height = 10*sqrt(15) m
area = 60*10*sqrt(15)m^2
=>600sqrt(15) m^2

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KAVITHA   9 years AGO

We can relate lenth f sides of triangle as s=1/2(40*80*60)=90
from diagonal its a triangle thus area of triangle is sqrt of(90*(90-40)*(90-80)*(90-60))=300sqrt15 metr sqr.
For a paralellogram 2*300sqrt 15 metr sqr=600*sqrt 15 metr sqr.

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vivek   9 years AGO

s=(40+60+80)/2=90
so required area is = 2*[90*30*50*10]^1/2=600 sqrt(15)m^2

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shiva gurram   9 years AGO

area of abcd=2area of abc
a=60,b=40,c=80
s=(a+b+c)/2
area of abc=sqrt(s(s-a)(s-b)(s-c))=3oosqrt(15)
area of parelleo(abcd)=600sqrt(15)

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m.lokeswari   9 years AGO

s=(a+b+d)/2
=(60+40+80)/2
=90
Area=2sqrt(s(s-a)(s-b)(s-c))
=2sqrt(90×30*50*10)
=600sqrt(15)

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SANTOSH   9 years AGO

by Hercules formula area of triangle one triangle is (area)^2=s(s-a)(s-b)(s-c) where s=(a+b+c)/2
==> area=300sqrt(15)
==> area of parallelogram is 600 sqrt(15)

Like? Yes (3) | No (1)  

Subha Natarajan   9 years AGO

Let ABCD be a parallelogram.. the area of the triangles separated by a diagonal will be equal.. the area of one triagle is 300sqrt(15) m^2..
therefore the area of the entire parallelogram is 2*300sqrt(15) which is equal to 600sqrt(15) m^2.

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SOMA NARESH   9 years AGO

the parallelogram with given two sides and diagonal is equal to two triangles of sides 40, 60, 80
So Area of parallelogram = twice that of area of triangle
area of triangle with sides a,b,c = Sqrt(s(s-a)(s-b)(s-c))
where s=(a+b+c)/2 = (40+60+80)/2 = 90
area of triangle = Sqrt(90*50*30*10)
=Sqrt(900*100*15)
= 30*10*Sqrt(15)
=300Sqrt(15)
Area of parallelogram = 2*300Sqrt(15)
=600Sqrt(15) m^2

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akshay kumar   9 years AGO

using hero's formula

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v v shyam kumar   9 years AGO

Here we will be calculating the area of two triangles,by adding those becomes the area of parallelogram.
Area of triangle is =Sqrt(s*s-a*s-b*s-c);
S=a+b+c/2;
a,b,c are sides of a triangle;
So s=80+40+60/2=90;
Area=Sqrt(90*10*50*30)=>300Sqrt(15);
Area of parallelogram =2times area of triangle.
2*300Sqrt(15)m^2;
Area =600Sqrt(15)m^2.

Like? Yes (3) | No (1)  

Snigdh Mayank   9 years AGO

let the height of parallelogram be h
let the foot of perpendicular be at a position x on the base.
then
h^2=40^2-x^2
h^2=80^2-(60-x)^2
solving we get h
so area is 60*h

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Piyush Telang   9 years AGO

Height of the Parallelogram = sqrt(1500) = 10 x sqrt(15)
Base of the Parallelogram = 60
Area of Parallelogram = Base x Height = 600 x sqrt(15)

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Kumar Ankur   9 years AGO

since two triangle are formed with same area i.e sides are 80m, 60m, 40m
Area of triangle is calculated with the help of heron's formula:-
s=80+40+60/2=90m
Area of triangle= sqrt s(s-a)s(s-b)(s-c)
on calculation we get s=300 sqrt (15)
hence, area of parallelogram=2* area of triangle=600 sqrt(15) m^2

Like? Yes (1) | No (1)  

RAVAL   9 years AGO

area of paralleleogram abcd=2* area of triangle abc
=2* sqrt(s*(s-a)*(s-b)*(s-c))
=2* 1161.89 (s=half periphery of abc)
= 2323.079 m^2
=600 sqrt m^2

Like? Yes (2) | No (2)