Area of Parallelogram ABCD: Find the Correct Solution | 4*6=24? [Picture]

[zak100]

Homework Statement

Find the area of Parallelogram ABCD where AD=4 and CD=6 and angle ABC=125 degrees, tell whether the area is greater than 24 or not?
See the attached picture

Homework Equations

Area of Parallelogram = length * breadth

The Attempt at a Solution

Sol: 4 * 6 = 24
but answer is wrong.

Some body please guide me.

Zulfi.

 

[jedishrfu]

Review your formula for the area of a parallelogram.

The formula you wrote works for rectangles only.

https://en.wikipedia.org/wiki/Parallelogram

 

[zak100]

Hi,
Thanks for your response. This means that i have to first convert the parallelogram into a rectangle and then apply the formula of area of rectangle. Thanks.

Zulfi.

 

[SammyS]

Homework Statement

Find the area of Parallelogram ABCD where AD=4 and CD=6 and angle ABC=125 degrees, tell whether the area is greater than 24 or not?
See the attached pictureView attachment 205337

Homework Equations

Area of Parallelogram = length * breadth

The Attempt at a Solution

Sol: 4 * 6 = 24
but answer is wrong.

Some body please guide me.

Zulfi.

You gave the following formula.:

Area of Parallelogram = length × breadth​

What is the definition of the breadth of a parallelogram ?

 

[Mark44]

Hi,
Thanks for your response. This means that i have to first convert the parallelogram into a rectangle and then apply the formula of area of rectangle. Thanks.

No.
You have to find the distance between sides BC and AD. Drop a vertical line from point C and form a right triangle with CD as its hypotenuse. A little bit of right triangle trig will give you the altitude of this triangle, which you can use to find the area of the parallelogram.

 

[Buffu]

Homework Statement

Find the area of Parallelogram ABCD where AD=4 and CD=6 and angle ABC=125 degrees, tell whether the area is greater than 24 or not?
See the attached pictureView attachment 205337

Homework Equations

Area of Parallelogram = length * breadth

The Attempt at a Solution

Sol: 4 * 6 = 24
but answer is wrong.

Some body please guide me.

Zulfi.

Without calculating you can tell whether area is more than or less than 24.

 

[zak100]

Hi,
Thanks for your help. I found the solution for this prob. I can draw a perpendicular from point C in downward direction & join D to this line. Let the joining point be E. Now area of parallelogram = AD * CE. But CE is less than 6. So area is less than 24.

Zulfi.

 

[zak100]

Hi,
How are these people finding the area of parallelogram in straight forward method without doing any alteration in the parallelogram?
http://formulas.tutorvista.com/math/area-of-a-parallelogram-formula.html

Some body please explain me this?

Zulfi.

 

[Ray Vickson]

Hi,
How are these people finding the area of parallelogram in straight forward method without doing any alteration in the parallelogram?
http://formulas.tutorvista.com/math/area-of-a-parallelogram-formula.html

Some body please explain me this?

Zulfi.

What part do you not understand? The web page shows you exactly what $b$ and $h$ are, and it gives the area formula as $A = b h$. What could be simpler?

 

[zak100]

Hi,
Thanks for your response.
I am talking about this sort of alteration as shown in the attached figure and pointed to me by Mark44:

No.
You have to find the distance between sides BC and AD. Drop a vertical line from point C and form a right triangle with CD as its hypotenuse. A little bit of right triangle trig will give you the altitude of this triangle, which you can use to find the area of the parallelogram.

This is mentioned in the solution of the question also. Examples on the web page do not do this. For instance in Example 1, area should be less than 63 units squares if we modify the figure using technique mentioned in the solution and by Mark44. Kindly see the image in reply#11.Zulfi.

 

[zak100]

Hi,
I am able to understand this. Area = b * h (i.e. height). To find the height i have to construct a triangle from the parallelogram. The height of the triangle would be the value of h to be used in the formula. In the link (i.e. math tutorial web site) they are provided the height h so they are using it directly in the formula.

Thanks.

Zulfi.