Answer:
40 unit²
Step-by-step explanation:
If you are referring to the figure attached read on:
We know that the distance between two points can be computed using the formula:
[tex]d = \sqrt{(X_2-X_1)^{2} + (Y_2-Y_1)^{2}}[/tex]
We also know that the formula for the area of a rectangle is:
A = L x W
While the area of a parallelogram is:
A = b x h
In the figure the dimensions of the parallelogram is easy to get as the base is vertical and the height is horizontal parallel to the x and y axes.
The base is 6 units, and the height is 1 unit. So we multiply that:
A = 6 x 1 = 6 units²
As for the rectangle we need to use the distance formula because they are not parallel to the x and y axes.
First let's get the width, then the length.
[tex]L = \sqrt{(-6 - 2)^2+(-1-1)^{2} } \\\\ = \sqrt{(-8)^2 + (-2)^2}\\\\ = \sqrt{64 + 4}\\\\ =\sqrt{68} \\\\ = 8.25 units\\W = \sqrt{(-6 - -5)^2+(-1 - - 5)^2} \\\\ = \sqrt{(-1)^2+(4)^2} \\\\ =\sqrt{1 + 16}\\\\ = \sqrt{17}\\\\ = 4.12 units\\[/tex]
So now we have the the dimensions of the rectangle, we can solve for the area.
A = 8.25 unit x 4.12 unit
= 33.99unit²
To get the total area then, we add up their areas:
33.99 unit² + 6 unit² = 39.99 unit² ≅ 40 units²
