Question

Good morning I really need some help with this problem please!

Answer 1

On the plane

Therefore, AB and DC are parallel sides, and so are BC and AD.

We need to calculate the length of 2 perpendicular sides, for example, AB and BC.

In general, the formula to get the distance between two points is

`\begin{gathered} (x_1,y_1),(x_2,y_2) \\ \Rightarrow d=√((x_1-x_2)^2+(y_1-y_2)^2) \end{gathered}`

Thus, in our case,

`d(AB)=√((-3+2)^2+(1+1)^2)=√(1+4)=√(5)`

and

`d(BC)=√((-2-2)^2+(-1-1)^2)=√(16+4)=√(20)`

Therefore, the area is

`\begin{gathered} \Rightarrow A=d(AB)*d(BC)=√(5)*√(20)=√(5*20)=√(100)=10 \\ \Rightarrow A=10 \end{gathered}`

Thus, the area is 10, option B.