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Answer:
<em>The area of the triangle DEF is 10.</em>
Step-by-step explanation:
<u>Area of a Triangle:</u>
A triangle of base B and height H (both must be perpendicular) has an area of:

The image below shows the triangle formed by the points DEF. It's important to notice the points E and F lie on the same horizontal line because they both have the same y-coordinate.
This fact simplifies the calculations since we can easily compute the length the of base as the difference of their x-coordinates:
B=3-(-2)=3+2=5
Being the base of a horizontal line, the height of the triangle can be calculated as the difference of y-coordinates of D and the height of that line.
H=2-(-2)=4
With these two values, we calculate the area:

The area of the triangle DEF is 10.
Answer:
Explained below.
Step-by-step explanation:
The formula for the interior angle of any regular polygon is given as;
Interior Angle = 180(n - 2)/n
Where n is number of sides
We are told the interior angle is 40°
Thus;
180(n - 2)/n = 40
Cross multiply to get;
180n - 360 = 40n
180n - 40n = 360
140n = 360
n = 360/140
n = 2.57
Number of sides of a regular polygon cannot be in decimal nor can it have less than 3 sides.
Thus, a shape with interior angle of 40 cannot be a polygon.