Question

What is the area of a rectangle with vertices at (−3, −1) , (1, 3) , (3, 1) , and (−1, −3) ?

Answer 1

The length of the side joining points (-3, -1) and (1, 3) is given by

$l= \sqrt{(1+3)^2+(3+1)^2} \\ \\ = \sqrt{4^2+4^2} = \sqrt{16+16} \\ \\ = \sqrt{32}$

The length of the side joining points (1, 3) and (3, 1) is given by

$w= \sqrt{(3-1)^2+(1-3)^2} \\ \\ = \sqrt{2^2+(-2)^2} = \sqrt{4+4} \\ \\ = \sqrt{8}$

The area of a rectangle is given by length times width.

Thus, the area of the given rectangle is given by

$Area=l\times w \\ \\ = \sqrt{32} \times \sqrt{8} \\ \\ = \sqrt{32\times8} = \sqrt{256} \\ \\ =\bold{16} \ units^2$

Answer 2

Hiya,

So I did this quiz just now and I have the answers. c:


1.) What is the area of a rectangle with vertices at 

(−3, −1)(−3, −1) , (1, 3)(1, 3) , (3, 1)(3, 1) , and (−1, −3)(−1, −3) ?

Enter your answer in the box. Do not round any side lengths.

Answer: 16 Units

2.) What is the perimeter of the rectangle shown on the coordinate plane, to the nearest tenth of a unit?

Answer: 26.8 Units

3.) What is the area of a triangle with vertices at 

(0, −2) ,  ​ (8, −2) ​ , and ​ (9, 1) ​ ?

Enter your answer in the box.

Answer: 12 Units

4.) What is the perimeter of the triangle shown on the coordinate plane, to the nearest tenth of a unit?
Answer: 21.6 Units

5.) What is the perimeter of a polygon with vertices at 

(−2, 1) , ​ (−2, 4) ​,  (2, 7) , ​ (6, 4) ​, and (6, 1) ​?

Enter your answer in the box. Do not round any side lengths.​

Answer: 24 Units

I really hope this helps! Let me know if it did... or anyone else that used this info!