Question

The four points (−2, 5), (−2, −1), (6, −1), and (3, 5) are the vertices of a polygon. What is the area, in square units, of this polygon?

Answer 1

Answer:

39 square units

Step-by-step explanation:

Answer 2

Look at the picture.

The polygon is a right-angled trapezoid.

The area is:
$A=\frac{a+b}{2} \times h$

The points (-2,-1) and (6,-1) lie on the same horizontal line, so the distance between them is 6-(-2)=6+2=8. The length of a is 8 units.
The points (-2,5) and (3,5) lie on the same horizontal line, so the distance between them is 3-(-2)=3+2=5. The length of b is 5 units.
The points (-2,5) and (-2,-1) lie on the same vertical line, so the distance between them is 5-(-1)=5+1=6. The length of h is 6 units.

$A=\frac{8+5}{2} \times 6=\frac{13}{2} \times 6=13 \times 3=39$

The area is 39 square units.