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the vertices of a polygon are (1,2) (1,6) (7,6) (7,2) (5,0) (3,0) graph the polygon then find its area

the vertices of a polygon are (1,2) (1,6) (7,6) (7,2) (5,0) (3,0) graph the polygon-example-1

1 Answer

6 votes

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.

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