What is the area of a rectangle with vertices at (−4, 0), (−3, 1) , (0, −2), and (−1, −3)? Enter your answer in the box. Do not round any side lengths.

Question

asked Nov 4, 2021 41.6k views

1 Answer

Pablo Boswell · Answer 1 · 2021-11-09T18:36:51+0000

Given :

Vertices of triangle (−4, 0), (−3, 1) , (0, −2), and (−1, −3).

To Find :

The area of a rectangle.

Solution :

Breadth of triangle :

$B = √((-4-(-3))^2+(0-1)^2)\\\\B = √(1^2+1^2)\\\\B = √(2)\ units$

Length of triangle :

$L = √((-4-0)^2+(0-(-2))^2)\\\\L = √(16+4)\\\\L = 2√(5)\ units$

Now, area is given by :

A = L×B

A = √2×2√5

A = 2√10 units

Therefore, the area is 2√10 units.

Hence, this is the required solution.