Question

Polygon ABCD is a rectangle. What is its area? Round your answer to the nearest tenth.

Answer 1

Answer: The correct option is A.

Step-by-step explanation:

To calculate the distance between the points, we use the formula:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

where,

d= distance

$x_2\text{ and }x_1$ are the coordinates of the points on x-axis

$y_2\text{ and }y_1$ 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)

• Calculating the distance CD:

$x_2=3\\x_1=-3\\y_2=2\\y_1=0$

Putting values in above equation, we get:

$CD=\sqrt{(3-(-3))^2+(2-0)^2}\\\\d=\sqrt{36+4}=6.32units$

• Calculating the distance AD:

$x_2=-4\\x_1=-3\\y_2=3\\y_1=0$

Putting values in above equation, we get:

$AD=\sqrt{(-4-(-3))^2+(-3-0)^2}\\\\d=\sqrt{1+9}=3.16units$

To calculate the area of a reactangle, we use the equation:

$Area=l\times b$         ....(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:

$Area=6.32\times 3.16\\\\Area=20.0 \text{ square units}$

Hence, the correct option is A.