by tommywallach Mon Jun 09, 2014 11:23 pm
Hey Anisha,
The definition of a parallelogram is that the two sets of sides are parallel. So we know that that 4 x 2 triangle on the right is also on the left, so the area is just base times height.
Area = base * height = 4 * 12 = 48
For the perimeter, we need to solve the right triangle's hypotenuse using Pythagoras. 4^2 + 2^2 = x^2 --> 16 + 4 = x^2 --> 20 = x^2 --> x=rt. 20 --> x = 2 * rt. 5
Now we know the perimeter is made up of two sides that are 2 * rt. 5 and two sides that are 12, so the perimeter is 24 + 4 rt. 5
Finally for finding the diagonal, draw a line down from point B that meets the base of the parallelogram at a right angle. We know the height of that new right triangle is 4, and the base is 10 (that's because it's 12 - 2, because it's two on the left side just as it's two on the right side).
4 ^ 2 + 10 ^ 2 = x ^ 2 --> 16 + 100 = x ^2 --> x = rt. 116 --> 2 * rt. 29
Hope that helps!
-t