N 9-1,10, P (2,1), Q (-2,2), R ( -1,-2). Find the area of the polygon with the given vertices

Answer 1

I assume that you meant

N (-1,1), P (2,1), Q (-2,2), R ( -1,-2)

The polygon NPQR is a quadrilateral. In order to calculate its area, let us break it into two triangles: NPR and NRQ. The two triangles share a base (NR). The base NR is parallel to the Y-axis, and its length is 3.

Now we need to find the heights of the triangles. The height of the triangle NPR (the distance between the point P and the line x = -1, where the points N and R are located) is 3.

Thus the area of the triangle NPR is 9 / 2

The height of the triangle NQR (the distance between the point Q and the line x = -1, where the points N and R are located) is 1.

Thus the area of the triangle NQR is 3 / 2

Thus the area of the polygon NPRQ is 9 / 2 + 3 / 2 = 12 / 2 = 6