
Concept explainers
(a)
To show:
If
Solution:
Explanation:
1) Concept:
The area of region
2) Given:
The line segment
3) Calculation:
The parametric equation for line segmentconnecting point
Hence proved
Conclusion:
(b)
To show:
That the area of the polygon is
Solution:
Explanation:
1) Concept:
By Green’s Theorem the area of region
2) Given:
The vertices of polygon in a counterclockwise order are
3) Calculation:
Apply Green’s Theorem to the path
where
Using the concept,
Area of polygon,
Using the formula in part (a)
Conclusion:
(c)
To find:
The area of pentagon with the given vertices
Solution:
Explanation:
1) Concept:
Formula from part (b)
2) Given:
The pentagon with vertices
3) Calculation:
Using the formula, Area is
Thus, area is
Conclusion:

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