Can someone please help me through this problem? I am not even really sure where I should start.

Quadrilateral ABCD has vertices A(-2,-2), B(1,4), C(8,4), D(5,2). Find the area of the quadrilateral, round your answer to the nearest tenth if necessary.

  • $\begingroup$ What kind of quadrilateral is this? What are the side lengths? $\endgroup$ – David H Jun 6 '14 at 2:44
  • $\begingroup$ That is the problem that I am having. That is all the information that is given. $\endgroup$ – IHeartBunnies Jun 6 '14 at 2:46
  • $\begingroup$ Shoelace theorem problem! $\endgroup$ – Peter Woolfitt Jun 6 '14 at 2:46
  • $\begingroup$ Try drawing a diagram and see if you can split it into two triangles. $\endgroup$ – BlackAdder Jun 6 '14 at 2:46
  • $\begingroup$ @IHeartBunnies you were given four points. Just plot them on a graph and see what they look like. Then use the coordinates of the points and the distance formula to compute the side lengths. $\endgroup$ – David H Jun 6 '14 at 2:51

Hint: Partition your polygon so that you get a trapezoid and a triangle, like below.

enter image description here

Then apply your formulas for area of a triangle and area of a trapezoid.


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