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puteri [66]
3 years ago
8

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

polygon?
27 units2
33 units2
36 units2
51 units2

Mathematics
2 answers:
olga2289 [7]3 years ago
8 0
<h2>Answer:</h2>

The area of the given Polygon is:

                        36\ unit^2

<h2>Step-by-step explanation:</h2>

The polygon is in the shape of the trapezoid with two bases AB and CD and altitude as: AD

Now we know that the area of trapezoid is given by:

\text{Area}=\dfrac{1}{2}\times (\text{Sum of bases})\times \text{Altitude}

i.e.

Here

\text{Area}=\dfrac{1}{2}\times (AB+CD)\times AD

Now, we find the length of AB,CD and AD using distance formula.

A is located at (-2,5)

B at (3,5)

C at (5,-1)

D at (-2,-1)

AB=\sqrt{(-2-3)^2+(5-5)^2}\\\\i.e.\\\\AB=\sqrt{(-5)^2+0^2}\\\\i.e.\\\\AB=\sqrt{25}\\\\i.e.\\\\AB=5\ units

CD=\sqrt{(5-(-2))^2+((-1)-(-1))^2}\\\\i.e.\\\\CD=\sqrt{7^2+0^2}\\\\i.e.\\\\CD=7\ units

AD=\sqrt{(-2-(-2))^2+(5-(-1))^2}\\\\i.e.\\\\AD=\sqrt{0^2+6^2}\\\\i.e.\\\\AD=6\ units

Hence, the area of  Trapezoid is:

Area=\dfrac{1}{2}\times (5+7)\times 6\\\\i.e.\\\\Area=36\ unit^2

pav-90 [236]3 years ago
3 0

Answer:

the area, in square units, of this polygon is 36 units2

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