Question

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

nearest tenth.
(2, 5)
(-4, 3)
(-3, 0)
(3, 2)

A. 20.0 square units
B. 19.0 square units
C. 25.6 square units
D. 39.7 square units​

Answer 1

Option A. 20.0 square units

Explanation:

Let

`A(2, 5),B(-4, 3),C(-3, 0),D(3, 2)`

Plot the points

see the attached figure

The area of the rectangle is equal to

`A=AB*AD`

the formula to calculate the distance between two points is equal to

`d=\sqrt{(y2-y1)^(2)+(x2-x1)^(2)}`

step 1

Find the distance AB

`A(2, 5),B(-4, 3)`

substitute in the formula

`AB=\sqrt{(3-5)^(2)+(-4-2)^(2)}`

`AB=\sqrt{(-2)^(2)+(-6)^(2)}`

`AB=√(40)\ units`

step 2

Find the distance AD

`A(2, 5),D(3, 2)`

substitute in the formula

`AD=\sqrt{(2-5)^(2)+(3-2)^(2)}`

`AD=\sqrt{(-3)^(2)+(1)^(2)}`

`AD=√(10)\ units`

step 3

Find the area of rectangle

`A=AB*AD`

we have

`AB=√(40)\ units`

`AD=√(10)\ units`

substitute

`A=(√(40))*(√(10))`

`A=20\ units^(2)`