Question

the vertices of a rectangle are located at (1, 2) (5, 0) (2, -6) and (-2, -4) what is the area of the rectangle

Answer 1

Area: 30

Explanation:

The area of a rectangle is given by the product between length (L) and width (W) of the rectangle:

`A=L\cdot W`

Here we have to find the length and the width of the rectangle.

We know the 4 vertices of the rectangle:

A (1,2)

B (5,0)

C (2,-6)

D (-2,-4)

The length can be calculated as the distance between two consecutive points of the rectangle. Choosing A and B, we find:

`L=|AB|=√((5-1)^2+(0-2)^2)=√(4^2+(-2)^2)=√(16+4)=4.47`

While the width can be calculating as the distance between the following pair of consecutive points, therefore the distance between B and C:

`W=|BC|=√((2-5)^2+(-6-0)^2)=√(3^2+(-6)^2)=√(9+36)=6.71`

And therefore, the area of hte rectangle is:

`A=L\cdot W=(4.47)(6.71)=30`