Question

Help me out!!What is the area of the polygon in square units?

A four quadrant graph with an irregular polygon with vertices at negative four comma eight, five comma eight, five comma two, nine comma two, twelve comma negative six, and negative four comma negative six.
68 square units
70 square units
72 square units
80 square units

Answer 1

• D) 80 square units

Explanation:

It is easy to find the area if we simplify the task.

Split the polygon into trapezoid and triangle by adding imaginary line y = 2 parallel to the x-axis.

Now find the area of each part.

Trapezoid

It has parallel bases:

• 0 - (-8) = 8 units and
• 4 - (-8) = 12 units

Its height is:

• 4 - 2 = 2 units

The area is:

• A = (b₁ + b₂)h/2 = (8 + 12)*2/2 = 20 units²

Triangle

It has base:

• 4 - (-8) = 12 units

Height:

• 2 - (-8) = 10 units

The area is:

• A = bh/2 = 12*10/2 = 60 units²

Total area

of the polygon is:

• 20 + 60 = 80 units²

Correct choice is D