Question

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

Answer 1

Answer:

The area of the given Polygon is:

                        $36\ unit^2$

Step-by-step explanation:

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:

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

Answer 2

Answer:

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