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Sagot :
Answer:
100 Square Units
Step-by-step explanation:
I took the test, it's the correct answer.
The area of the quadrilateral is 100 square units.
What is a quadrilateral?
A quadrilateral is a two-dimensional geometrical figure that has four sides, four vertices, and four interior angles.
The vertices of the given quadrilateral are P(3,7), Q(7,15), R(17,10), S(13,2).
Therefore, the length of the side PQ is
[tex]= \sqrt{(15-7)^{2}+(7-3)^{2}} units\\= \sqrt{8^{2}+4^{2}} units\\= \sqrt{64+16} units\\= \sqrt{80} units[/tex]
The length of the side QR is
[tex]= \sqrt{(10-15)^{2}+(17-7)^{2}} units\\= \sqrt{(-5)^{2}+(10)^{2}} units\\= \sqrt{25+100} units\\= \sqrt{125} units[/tex]
The length of the side RS is
[tex]= \sqrt{(2-10)^{2}+(13-17)^{2}} units\\= \sqrt{(-8)^{2}+(-4)^{2}} units\\= \sqrt{64+16} units\\= \sqrt{80} units[/tex]
The length of the side SP is
[tex]= \sqrt{(7-2)^{2}+(3-13)^{2}} units\\= \sqrt{(5)^{2}+(-10)^{2}} units\\= \sqrt{25+100} units\\= \sqrt{125} units[/tex] (ignoring the negative terms for all the sides)
Therefore, the opposite sides of the quadrilateral are equal.
Slope of the line PQ is
[tex]m_{1} = \frac{15-7}{7-3} = \frac{8}{4} = 2[/tex]
Slope of the line SP is
[tex]m_{2} = \frac{2-7}{13-3} = \frac{-5}{10} = - \frac{1}{2}[/tex]
Therefore, the slope of line PQ = (-1)/the slope of line SP
Hence, line PQ and line SP are perpendicular.
Therefore, the quadrilateral is a rectangle.
Now, the area of the quadrilateral is
[tex]= (\sqrt{80})(\sqrt{125})[/tex] square units
[tex]= 100[/tex] square units
Learn more about a quadrilateral here: https://brainly.com/question/19337593
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