parallelogram angle

[jeevan.Gk]

Each side of a certain parallelogram has length 6 . If the area is 18.
Which of the following is the measure of one of its angles.

a. 30
b. 45
c. 60
d. 90
e. 120

[logitech]

So the area is 18

6 x HEIGHT = 18

HEIGHT = 3 from the graph you can see that it is a 3-6-3sqrt(3) triangle with 30,60, 90 degrees

So I would choose A) 30

[Rashmi1804]

Logitech,

The area given here is the area of the parallellogram {rhombus} right ??
So how can it be 6*ht = 18 ??

Area of the rhombus = 1/2 * product of the diagnols of the rhombus....

Could you please explain your solution in details ??

[DanaJ]

Rashmi1804: A rombus is a parallelogram equal sides. A parallelogram only has pairs of equal sides. This is why the formula for the area provided by logitech is correct.

[Rashmi1804]

DanaJ ..I still dint understand how the area is equal to ht *one of the sides...

if it is area= l*b then it is be 6*6 = 36 ...isnt it ?

I checked out for formulae to calc area of the rhombus....all i got is area is half of product of it's diagnols

Okiee....temme onething....area of a square with s=6 and area of a rhombus with s=6 are not equal...are they ??

[Stuart@KaplanGMAT]

DanaJ ..I still dint understand how the area is equal to ht *one of the sides...

if it is area= l*b then it is be 6*6 = 36 ...isnt it ?

I checked out for formulae to calc area of the rhombus....all i got is area is half of product of it's diagnols

Okiee....temme onething....area of a square with s=6 and area of a rhombus with s=6 are not equal...are they ??

A rhombus is a parallelogram, just like a square and a rectangle are both parallelograms. The area of any parolellogram is base * height, which is only the same as length times base for squares and rectangles (because of the 90 degree angles).

[moorthy76]

can we use the formula Area = side x side x sin of angle?

WE will get 6 x 6 x sin angle = 18

Sin angle = 1/2

Angle is 30.

Is this correct?