<u>Answer:</u> The correct option is A.
<u>Step-by-step explanation:</u>
To calculate the distance between the points, we use the formula:
![d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28x_2-x_1%29%5E2%2B%28y_2-y_1%29%5E2%7D)
where,
d= distance
are the coordinates of the points on x-axis
are the coordinates of the points on y-axis
For the given points:
A(-4,3), B(2,5), C(3,2) and D(-3,0)
- <u>Calculating the distance CD:</u>
![x_2=3\\x_1=-3\\y_2=2\\y_1=0](https://tex.z-dn.net/?f=x_2%3D3%5C%5Cx_1%3D-3%5C%5Cy_2%3D2%5C%5Cy_1%3D0)
Putting values in above equation, we get:
![CD=\sqrt{(3-(-3))^2+(2-0)^2}\\\\d=\sqrt{36+4}=6.32units](https://tex.z-dn.net/?f=CD%3D%5Csqrt%7B%283-%28-3%29%29%5E2%2B%282-0%29%5E2%7D%5C%5C%5C%5Cd%3D%5Csqrt%7B36%2B4%7D%3D6.32units)
- <u>Calculating the distance AD:</u>
![x_2=-4\\x_1=-3\\y_2=3\\y_1=0](https://tex.z-dn.net/?f=x_2%3D-4%5C%5Cx_1%3D-3%5C%5Cy_2%3D3%5C%5Cy_1%3D0)
Putting values in above equation, we get:
![AD=\sqrt{(-4-(-3))^2+(-3-0)^2}\\\\d=\sqrt{1+9}=3.16units](https://tex.z-dn.net/?f=AD%3D%5Csqrt%7B%28-4-%28-3%29%29%5E2%2B%28-3-0%29%5E2%7D%5C%5C%5C%5Cd%3D%5Csqrt%7B1%2B9%7D%3D3.16units)
To calculate the area of a reactangle, we use the equation:
....(1)
where,
l = length of the rectangle = CD = 6.32 units
b = breadth of the rectangle = AD = 3.16 units
Putting values in equation 1, we get:
![Area=6.32\times 3.16\\\\Area=20.0 \text{ square units}](https://tex.z-dn.net/?f=Area%3D6.32%5Ctimes%203.16%5C%5C%5C%5CArea%3D20.0%20%5Ctext%7B%20square%20units%7D)
Hence, the correct option is A.