Question

What is the area of the rectangle? shoe your work! do not round anything until the very end and round your final answer to the tenths place.

Answer 1

The area of the rectangle is 42 units^2

Explanation:

we know that

The area of rectangle is equal to

`A=LW`

In this problem

AB=DC

BC=AD

see the attached figure with letters to better understand the problem

we have that

`L=BC\\W=AB`

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

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

we have the points

`A(2,-1),B(5,2),C(12,-5),D(9,-8)`

Find out the distance BC

we have

`B(5,2),C(12,-5)`

substitute in the formula

`d=\sqrt{(-5-2)^(2)+(12-5)^(2)}`

`d=\sqrt{(-7)^(2)+(7)^(2)}`

`d_B_C=√(98)\ units`

Find out the distance AB

we have

`A(2,-1),B(5,2)`

substitute in the formula

`d=\sqrt{(2+1)^(2)+(5-2)^(2)}`

`d=\sqrt{(3)^(2)+(3)^(2)}`

`d_A_B=√(18)\ units`

Find out the area

`A=(L)(W)`

we have

`L=d_B_C=√(98)\ units`

`W=d_A_B=√(18)\ units`

substitute

`A=(√(98))(√(18))=42.0\ units^2`