Question

What is the area of this polygon?

Answer 1

Answer:

  34.5 units²

Step-by-step explanation:

There are methods for finding the area of a polygon using arithmetic on the coordinates. Here, it is probably more convenient to cut the figure into two triangles and a trapezoid and figure the areas of those.

A line from (-5, 1) to (1, 1) will create a triangle above that line with base 6 and height 3. Its area will be ...

   A = 1/2·b·h = 1/2·6·3 = 9 . . . units²

Similarly, a line from (1, 1) to (1, -2) will create a triangle to the right of that line with base 3 and height 4. Its area will be ...

  A = 1/2·b·h = 1/2·3·4 = 6 . . . units²

The remaining trapezoid has top base 6, bottom base 7, and a height of 3. Its area will be ...

  A = 1/2·(b1+b2)·h = 1/2·(6 +7)·3 = 39/2 = 19.5 . . . units²

Then the total area of the figure is ...

  (9 + 6 + 19.5) units² = 34.5 units²