Answer:
32 square units
Explanation:
You want the area of a polygon with the vertices (1,2) (1,6) (7,6) (7,2) (5,0) (3,0).
Composition
The graphed figure can be decomposed into a rectangle 4 units high and 6 units wide, together with a trapezoid with bases 6 and 2, and height 2.
Formulas
The area formulas for these parts are ...
A = HW . . . . area of a rectangle of height H and width W
A = 1/2(b1 +b2)h . . . . area of a trapezoid with bases b1, b2, and height h
Application
The rectangle area is ...
A = (4)(6) = 24
The trapezoid area is ...
A = 1/2(6+2)(2) = 8
So, the total area of the polygon is ...
A = 24 +8 = 32 . . . . square units.
The area of the polygon is 32 square units.