I'll answer question 2
Answer: 600,000 square miles
Note: you may need to erase the comma if you are typing this answer into a computer system.
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Explanation:
Draw a line segment from point B to point D. This divides the quadrilateral into two triangles ABD and BCD.
Refer to the attached image below. First look at figure 1.
This shows triangle ABD with base AD = 800 and height 300. The height is the vertical distance from point B to the x axis. Note how point B is 300 units above the x axis. The height is shown in blue, and the height is always perpendicular to the base.
The area of triangle ABD is...
area = (base*height)/2 = (800*300)/2 = 120,000 square miles
We'll use this later.
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Now refer to figure 2 in the attached images.
This shows triangle BCD. It has base CD = 800. It might help to rotate the triangle so that CD is horizontal. The height, shown in blue, is perpendicular to the base. It is 1200 units because we span from x = -800 to x = 400 which is a total horizontal distance of |-800-400| = 1200
The area of triangle BCD is....
area = (base*height)/2 = (800*1200)/2 = 480,000 square miles
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Lastly, we'll add up the two triangular areas we found
area of quadrilateral ABCD = (area of triangle ABD) + (area of triangle BCD)
area of quadrilateral ABCD = (120,000 sq mi) + (480,000 sq mi)
area of quadrilateral ABCD = 600,000 square miles
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