ABCD is a regular paralleogram, A=(2,1) B=(7,2) and C=(4,6), work out the gradient of the line CD and then work out the area of ABCD.

As its a parallelogram the gradient of CD will be the same as the gradient of AB so you just need to work out the gradient of AB using the formula (y₂-y₁)/(x₂-x₁) which would be (2-1)/(7-2)= 1/5 or 0.2.To find the area you need the base which you can find using Pythagoras' theorem and the coordinates of points A and B, square root of (y₂-y₁)²+ (x₂-x₁)² so square root of 26 times by height which is difference in y coordinate between A and C so 5. this gives an answer of 5 root 26.