Find the area of a parallelogram with the given vertices.

Question

P(2,3) Q(4,3) R(8,8) S(10,8)

Answer 1

 If you look at the points, you'll notice some similarities and differences. x-values are: 2, 4, 10, and 8. 2 and 4 have the same y-value, and their difference is 2. 8 and 10 have the same y-value and their difference is also 2. 

So we know at least one side has a length of 2.

 

Use the same process for y's and you find the height to be 5. 

 

A = b*H

A = (2)(5)

A = 10

 

Ta-da!

 

If you need clarification or have more questions, let me know. I'd love to help you out more.

Answer 2

The four points are the vertices of a parallelogram.  Note that P and Q share a y value (of 3) and the length of that side is 2; the points R and S share a y value ( of 8) and the length of that side also is 2,

 

The height of the parallelogram is 5 (if the base is PQ).

 

The area of a parallelogram is A = bh

So, for this parallelogram, the Area = 2*5 = 10