What is the area of this parallelogram?

In summary, the teacher has taught the students of ways to find the area of a triangle from its side lengths, but has not mentioned Heron's Formula. The students can also solve the problem using vectors, and can find the area of a square by subtracting the areas of its four triangles.
  • #1
eXoo
4
0
1. I'll illustrate the question, I've been having a lot of troubles with it, the image is in the attachements.

2. I've tried it many times, with different methods but keep getting different answers. Really need help with it. Most recently tried by splitting it into two triangles then working out from there, got 12.86, but it's most likely wrong.

Thanks :)
 

Attachments

  • 385518_10150446665764539_690944538_8411976_1727372038_n.jpg
    385518_10150446665764539_690944538_8411976_1727372038_n.jpg
    7.8 KB · Views: 454
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  • #2
if you know about determinants then take the determinant of the matrix with the vectors AB and BL in it's rows

other wise, try constructing a rectangle of length 5.3 and height 5.2 and take some squared and triangles away

ask again if you need another hint
 
  • #3
genericusrnme said:
if you know about determinants then take the determinant of the matrix with the vectors AB and BL in it's rows

other wise, try constructing a rectangle of length 5.3 and height 5.2 and take some squared and triangles away

ask again if you need another hint

My teacher has taught us neither of those ways, so I don't really know how to get a result with them. :(
 
  • #4
if you can calculate the area of a triangle and a rectangle you'll be able to find the area by constructing a rectangle and cutting parts out of it

if you set it up and play about for a bit you should be able to see what parts to cut out and from then on it's pretty basic calculations
 
  • #5
genericusrnme said:
if you can calculate the area of a triangle and a rectangle you'll be able to find the area by constructing a rectangle and cutting parts out of it

if you set it up and play about for a bit you should be able to see what parts to cut out and from then on it's pretty basic calculations

still don't get it :(
 
  • #6
If you draw a diagonal you have two similar triangles. Further, you can find the lengths of all the sides of the triangles.

What methods do you know for finding the area of a triangle from its side lengths? Have you heard of Heron's Formula? (You should have come across it in high school math)

You can also solve the problem using vectors: The cross product of two (non parallel) vectors in a plane yields a vector whose magnitude is the area of the parallelogram with those vectors forming two of its sides.
 
Last edited:
  • #7
Look at my attachment, hopefully that should help
calculate the area of the square and take away parts to find the area of your parallelogram
 

Attachments

  • imgage.JPG
    imgage.JPG
    10.2 KB · Views: 419
  • #8
I think this is what genericusrnme was getting at. The attachment shows the parallelogram enclosed inside a rectangle. Find the area of the rectangle, and then subtract the areas of the four triangles, and you'll get the area of the parallelogram.EDIT: Beaten to it. :biggrin:
 

Attachments

  • Parallelogram.jpg
    Parallelogram.jpg
    9.3 KB · Views: 422
Last edited:

What is the formula for finding the area of a parallelogram?

The formula for finding the area of a parallelogram is base x height, or A = bh.

How do you calculate the area of a parallelogram if the height is not given?

If the height is not given, you can use the formula A = (length of one side) x (distance between that side and the opposite side).

Can you find the area of a parallelogram if only the angles are known?

Yes, if you know the measure of one angle and the lengths of the sides, you can use the formula A = ab sin(C), where a and b are the lengths of the sides and C is the measure of the angle.

What is the difference between a parallelogram and a rectangle when it comes to finding the area?

A rectangle is a special type of parallelogram with four right angles, so finding the area of a rectangle is simply base x height. For a parallelogram, the base and height are not necessarily perpendicular, so the formula is different (A = bh).

Can the area of a parallelogram be negative?

No, the area of a parallelogram cannot be negative because it is a measure of space and cannot have a direction. If you end up with a negative value when calculating the area, it is likely that you made a mistake in your calculations.

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