Two uniform parallelograms look like this:
The area of the blue-shaded area is...
NOTE: The shapes are not to scale in the image.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
We can start by calculating what K is.
K = 7 − 3 = 4
3 K = 3 4 = 1 . 3 3 3 . . . 1 . 3 3 3 . . . 3 = 2 . 2 5
Now using the Pythagorean Theorem, we can determine the height of the smaller parallelogram.
a 2 + b 2 = c 2 a = 3 − 2 c = 2 . 2 5 1 2 + b 2 = 2 . 2 5 2 b 2 = 5 . 0 6 2 5 − 1 b = 4 . 0 6 2 5 A T r i a n g l e = 2 b × 1 A T r i a n g l e = 2 2 . 0 1 5 5 . . . × 1 A T r i a n g l e = 1 . 0 0 7 7 8 . . . A T r i a n g l e > 1
You could also say if b 2 > 4 then b > 2 and therefore the area will be greater than 1.